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  4. MTH603 - Numerical Analysis
  5. MTH603 Mid Term Past and Current Solved Paper Discussion
dy/dx - = 1 - y,y(0) = 0 is an example of
L
dy dx = 1 - y,y(0) = 0 is an example of Answer An ordinary differential equation A partial differential equation A polynomial equation None of the given choices
MTH603 - Numerical Analysis
In Double integration, the interval [a, b] should be divided into [c, d) should be divided into --sub intervals of size k. --subintervals of size h and the interval
zaasmiZ
In Double integration, the interval [a, b] should be divided into [c, d) should be divided into --sub intervals of size k. --subintervals of size h and the interval Answer equal, equal equal, unequal unequal, equal unequal, unequal
MTH603 - Numerical Analysis
The (n + 1) th difference of a polynomial of degree n is...
Kevin AustinK
The (n + 1) th difference of a polynomial of degree n is… Answer 0 Constant n +1
MTH603 - Numerical Analysis
Let P be any real number and h be the step size of any interval. Then the relation between h and P for the backward difference is given by
G
Let P be any real number and h be the step size of any interval. Then the relation between h and P for the backward difference is given by Answer x-x, = Ph x- x, = P x + x, = Ph (x - x,)h= P
MTH603 - Numerical Analysis
In integrating $\int_{0}^{\frac{2}{2}} \cos x d x$ by dividing the interval into four equal parts, width of the interval should be
zaasmiZ
In integrating $\int_{0}^{\frac{2}{2}} \cos x d x$ by dividing the interval into four equal parts, width of the interval should be Answer $\frac{\pi}{2}$ $\pi$ $\frac{\pi}{8}$
MTH603 - Numerical Analysis
In fourth order Runge-Kutta method K 4
zaasmiZ
In fourth order Runge-Kutta method K 4 is given by Answer k4 = hf(xn th,yn + kz) k4 = hf(xn + 2h, + 2kz) None of the given choices k4 = hf(x, — h,Yn — kz)
MTH603 - Numerical Analysis
In fourth order Runge-Kutta method k2
zaasmiZ
In fourth order Runge-Kutta method k2 is given by Answer ^2-“/”“” З’Уп 3’ k2 = 45(-12.30-42)
MTH603 - Numerical Analysis
What is the Process of finding the values outside the interval (Xo,x,) called?
zaasmiZ
What is the Process of finding the values outside the interval (Xo,x,) called? Answer interpolation iteration Polynomial equation extrapolation
MTH603 - Numerical Analysis
When we apply Simpson's 3/8 rule, the number of intervals n must be
zaasmiZ
When we apply Simpson’s 3/8 rule, the number of intervals n must be Answer Even Odd Multiple of 3 Page 177 Similarly in deriving composite Simpson’s 3/8 rule, we divide the interval of integration into n sub-intervals, where n is divisible by 3, and applying the integration formula Multiple of 8
MTH603 - Numerical Analysis
Milne's P-C method is a multi step method where we assume that the solution to the given initial value problem is known at past --equally spaced points.
zaasmiZ
Milne’s P-C method is a multi step method where we assume that the solution to the given initial value problem is known at past –equally spaced points. Answer 2 1 3 4 1
MTH603 - Numerical Analysis
The truncation error in Adam's predictor formula is ....-times more than that in corrector formula
zaasmiZ
The truncation error in Adam’s predictor formula is …-times more than that in corrector formula Answer 10 11 12 13
MTH603 - Numerical Analysis
To apply Simpson's 3/8 rule, the number of intervals be
zaasmiZ
Answer 10 11 12 13
MTH603 - Numerical Analysis
Which formula is useful in finding the interpolating polynomial?
zaasmiZ
Given the following data Which formula is useful in finding the interpolating polynomial? Answer Lagrange’s interpolation formula X 1 2 5 9 f(x) 2 0 30 132 Page 135 Newton’s forward difference interpolation formula Newton’s backward difference interpolation formula None of the given choices
MTH603 - Numerical Analysis
Rate of change of any quantity with respect to another can be modeled by
zaasmiZ
Answer An ordinary differential equation A partial differential equation A polynomial equation None of the given choices
MTH603 - Numerical Analysis
Romberg's integration method is ------ than Trapezoidal and Simpson's rule.
zaasmiZ
Answer more accurate less accurate equally accurate none of the given choices
MTH603 - Numerical Analysis
In integrating f, e2* dx by dividing into eight equal parts, width of the interval should be......
zaasmiZ
Answer 0.250 0.500 0.125 0.625
MTH603 - Numerical Analysis
To apply Simpson's 1/3 rule, valid number of intervals are?
zaasmiZ
7 8 5 3 Page 177 The Simpson’s 1/3 rule, we have used two sub-intervals of equal width. In order to get a composite formula, we shall divide the interval of integration [a, b] Into an even number
MTH603 - Numerical Analysis
Newton's divided difference interpolation formula is used when the values of the independent variable are
zaasmiZ
Equally spaced Not equally spaced Constant None of the above
MTH603 - Numerical Analysis
If there are (n+1) values of y corresponding to (n+1) values of x, then we can represent the function f(x) by a polynomial of degree
zaasmiZ
If there are (n+1) values of y corresponding to (n+1) values of x, then we can represent the function f(x) by a polynomial of degree
MTH603 - Numerical Analysis
MTH603 Assignment 1 Solution and Discussion
cyberianC
Re: MTH603 Assignment 1 Solution and Discussion Assignment No. 1 MTH603 (Spring 2022) Total Marks: 20 Due Date: 8th June, 2022 DON’T MISS THESE: Important instructions before attempting the solution of this assignment: • To solve this assignment, you should have good command over 1-8 lectures. • Upload assignments properly through the LMS, No Assignment will be accepted through email. • Write your ID on the top of your solution file. Don’t use colored backgrounds in your solution files. Use Math Type or Equation Editor, etc. for mathematical symbols. You should remember that if the solution files of some students are finding the same (copied), we will reward zero marks to all those students. Make a solution by yourself and protect your work from other students, otherwise both original and copied assignments will be awarded zero marks. Also remember that you are supposed to submit your assignment in Word format, any other format like scanned images, etc. will not be accepted and be awarded zero marks Question 1 Find a real root of the equation 2x+cos⁡(x)+e^x=0 using Bisection Method using Newton Raphson Method Also compare the results and comment which of the methods performs better and which is worst. You will consider x_0=-0.6557 as a best approximation while comparing the roots. Note: In each of the above methods,you are required to perform three iterations. Spring 2022_MTH603_1.docx
MTH603 - Numerical Analysis

MTH603 Mid Term Past and Current Solved Paper Discussion

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mid termsolved papermth603 past papers midtermmth603 finalterm huge filemth603 solved papers by junaidmth603 solved papers by moaazmth603 by moaaz pdf downloadmth603 final term preparationmth603 final term mcqsmth603 mcqs pdf download
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  • zareenZ zareen

    Question # 1 of 10 (Total Marks: 1)
    While solving a system of linear equations, which of the following approach is economical for the computer memory?
    Select correct option:
    Direct
    Iterative (Page 69)
    Analytical
    Graphical

    Question # 2 of 10 (Total Marks: 1)
    The basic idea of relaxation method is to reduce the largest residual to …
    Select correct option:
    One
    Two
    Zero (Page 83)
    None of the given choices

    Question # 3 of 10 (Total Marks: 1)
    The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its
    ________.
    Select correct option:
    main diagonal (Page 104)
    last column
    last row
    first row

    Question # 4 of 10 (Total Marks: 1)
    If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix ,
    the eigenvalues of A are the diagonal entries of A.
    Select correct option:
    TRUE Click here for detail
    FALSE

    Question # 5 of 10 (Total Marks: 1)
    A 3 x 3 identity matrix have three and different eigen values.
    Select correct option:
    TRUE Click here for detail
    FALSE

    Question # 6 of 10 (Total Marks: 1)
    Which of the following is a reason due to which the LU decomposition of the system of linear equations;
    x+y = 1, x+y =2 is not possible?
    Select correct option:
    Associated coefficient matrix is singular
    All values of l’s and u’s can’t be evaluated
    Determinant of coefficient matrix is zero
    All are equivalent

    Question # 7 of 10 (Total Marks: 1)
    Gauss - Jordan Method is similar to …
    Select correct option:
    Gauss–Seidel method
    Iteration’s method
    Relaxation Method
    Gaussian elimination method (Page 95)

    Question # 8 of 10 (Total Marks: 1)
    While using Relaxation method, which of the following is the largest Residual for 1st iteration on the
    system; 2x+3y = 1, 3x +2y = - 4 ?
    Select correct option:
    -4
    3
    2
    1

    Question # 9 of 10 (Total Marks: 1)
    Gauss–Seidel method is also known as method of …
    Select correct option:
    Successive displacement (Page 263)
    Iterations
    False position
    None of the given choices

    Question # 10 of 10 (Total Marks: 1)
    Jacobi’s Method is a/an…
    Select correct option:
    Iterative method (Page 69)
    Direct method

    QUIZ.NO.1(2)

    Question # 1 of 10 (Total Marks: 1)
    The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the
    given 3 x 3 identity matrix. where symbol ^ shows power.
    Select correct option:
    (x-1)^3
    (x+1)^3
    x^3-1
    x^3+1

    Question # 2 of 10 (Total Marks: 1)
    The can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue
    the dominant eigenvalue of A.
    Select correct option:
    TRUE
    FALSE

    Question # 3 of 10 (Total Marks: 1)
    In … method, a system is reduced to an equivalent diagonal form using elementary
    transformations.
    Select correct option:
    Jacobi’s
    Gauss-Seidel
    Relaxation
    Gaussian elimination (Page 262)

    Question # 4 of 10 (Total Marks: 1)
    The linear equation: 2x+0y-2=0 has -------- solution/solutions.
    Select correct option:
    Unique (Page 48)
    no solution
    infinite many
    finite many

    Question # 5 of 10 (Total Marks: 1)
    Under elimination methods, we consider, Gaussian elimination and …methods.
    Select correct option:
    Gauss-Seidel
    Jacobi
    Gauss-Jordan elimination (Page 48)
    None of the given choices

    Question # 6 of 10 (Total Marks: 1)
    Which of the following method is not an iterative method?
    Select correct option:
    Jacobi’s method
    Gauss-Seidel method
    Relaxation methods
    Gauss-Jordan elimination method

    Question # 7 of 10 (Total Marks: 1)
    An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal
    to zero.
    Select correct option:
    TRUE
    FALSE (Page 97)

    Question # 8 of 10 (Total Marks: 1)
    Exact solution of 2/3 is not exists.
    Select correct option:
    TRUE
    FALSE

    Question # 9 of 10 (Total Marks: 1)
    When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the
    method is …
    Select correct option:
    Stable
    Unstable
    Convergent (Page 70)
    Divergent

    Question # 10 of 10 (Total Marks: 1)
    Gauss–Seidel method is similar to …
    Select correct option:
    Iteration’s method
    Regula-Falsi method
    Jacobi’s method
    None of the given choices (Page 263)

    QUIZ.NO.1(3)

    Question # 1 of 10 (Total Marks: 1)
    Sparse matrices arise in computing the numerical solution of …
    Select correct option:
    Ordinary differential equations
    Partial differential equations (Page 69)
    Linear differential equations
    Non-linear differential equations

    Question # 2 of 10 (Total Marks: 1)
    While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the
    system; x-2y =1, x+4y=4 ?
    Select correct option:
    (1, 0.75)
    (0,0)
    (1,0)
    (0,1)

    Question # 3 of 10 (Total Marks: 1)
    While solving a system of linear equations by Gauss Jordon Method, after all the elementary row
    operations if there lefts also zeros on the main diagonal then which of the is true about the system?
    Select correct option:
    System may have unique solutions
    System has no solution
    System may have multiple numbers of finite solutions
    System may have infinite many solutions

    Question # 4 of 10 (Total Marks: 1)
    Numerical methods for finding the solution of the system of equations are classified as direct and
    … methods
    Select correct option:
    Indirect
    Iterative (Page 48)
    Jacobi
    None of the given choices

    Question # 5 of 10 (Total Marks: 1)
    If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st
    iteration will reduce to -------.
    Select correct option:
    zero
    4
    -1
    -1

    Question # 6 of 10 (Total Marks: 1)
    While using Relaxation method, which of the following is the Residuals for 1st iteration on the system;
    2x+3y = 1, 3x +2y =4 ?
    Select correct option:
    (2,3)
    (3,-2)
    (-2,3)
    (1,4)

    0= 1-2x-3y
    0= 4-3x -2y

    Question # 7 of 10 (Total Marks: 1)
    If the order of coefficient matrix corresponding to system of linear equations is 33 then which of the
    following will be the orders of its decomposed matrices; ‘L’ and ‘U’?
    Select correct option:
    Order of ‘L’ = 3    1, Order of ‘U’ = 13
    Order of ‘L’ = 3    2, Order of ‘U’ = 2*3

    Order of ‘L’ = 33, Order of ‘U’ = 33
    Order of ‘L’ = 34, Order of ‘U’ = 43

    Question # 8 of 10 (Total Marks: 1)
    While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering
    is feasible to have good approximate solution?
    Select correct option:
    x+4y = 1, x-2y = 4
    x+2y = 1, x- 4y =4
    x+4y = 4, x–2y = 1
    no need to reordering

    Question # 9 of 10 (Total Marks: 1)
    Full pivoting, in fact, is more …than the partial pivoting.
    Select correct option:
    Easiest
    Complicated (Page 51)
    Question # 10 of 10 (Total Marks: 1)
    For the equation
    11fd5b6d-0b86-453d-83b2-64f970116bbc-image.png the root of the equation lies in the interval…

    ► (1, 3)
    ► (1, 2)
    ► (0, 1)
    ► (1, 2)

    QUIZ.NO.1(4)

    Question # 1 of 10 (Total Marks: 1)
    …lies in the category of iterative method.
    ► Bisection Method
    ► Regula Falsi Method
    ► Secant Method
    ► all of the given choices (Page 8)

    Question # 2 of 10 (Total Marks: 1)
    If n x n matrices A and B are similar, then they have the different eigenvalues (with the same
    multiplicities).
    True
    False

    Question # 3 of 10 (Total Marks: 1)
    The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its
    main diagonal.
    No Click here for detail
    At least one

    Question # 4 of 10 (Total Marks: 1)
    If the root of the given equation lies between a and b, then the first approximation to the root of the equation by bisection method is …
    b751921b-b3f6-45cd-9112-ad988bc16051-image.png

    Question # 5 of 10 (Total Marks: 1)
    To apply Simpson’s 3/8 rule, the number of intervals in the following must be
    ► 10
    ► 11
    ► 12
    ► 13

    Question # 6 of 10 (Total Marks: 1)
    The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite
    matrices A.
    Select correct option:
    Positive Click here for detail
    negative

    Question # 7 of 10 (Total Marks: 1)
    Differences methods find the ________ solution of the system.
    Select correct option:
    numerical
    Analytical

    Question # 8 of 10 (Total Marks: 1)
    To apply Simpson’s 1/3 rule, the number of intervals in the following must be
    ► 2 (Simpson’‘s 1/3 rule must use an even number of elements’)
    ► 3
    ► 5
    ► 7

    Question # 9 of 10 (Total Marks: 1)
    Bisection and false position methods are also known as bracketing method and are always
    Divergent
    Convergent (Page 26)
    .67

    Question # 10 of 10 (Total Marks: 1)
    The Inverse of a matrix can only be found if the matrix is
    Singular
    None Singular: Every square non-singular matrix will have an inverse.
    Scalar
    Diagonal

    QUIZ.NO.1(5)

    Question # 1 of 10 (Total Marks: 1)
    In interpolation is used to represent the δ
    Forward difference Δ
    Central difference (Page 117)
    Backward difference

    Question # 2 of 10 (Total Marks: 1)
    The base of the decimal system is _______
    10
    0
    2
    8
    None of the above.

    Question # 3 of 10 (Total Marks: 1)
    Bisection method is … method
    ► Open Method
    ► Bracketing Method (page 26)

    Question # 4 of 10 (Total Marks: 1)
    A 3 x 3 identity matrix have three and __________eigen values.
    same
    different

    Question # 5 of 10 (Total Marks: 1)
    Eigenvalues of a symmetric matrix are all _______ .
    Real (page 104)
    complex
    zero
    positive

    Question # 6 of 10 (Total Marks: 1)
    The Jacobi iteration converges, if A is strictly diagonally dominant.
    TRUE (Page 69)
    FALSE

    Question # 7 of 10 (Total Marks: 1)
    Below are all the finite difference methods EXCEPT _________.
    jacobi’s method
    newton’s backward difference method
    Stirlling formula
    Forward difference method

    Question # 8 of 10 (Total Marks: 1)
    Two matrices with the same characteristic polynomial need not be similar.
    TRUE
    FALSE

    Question # 9 of 10 (Total Marks: 1) No.69
    The determinant of a diagonal matrix is the product of the diagonal elements.
    True
    False

    Question # 10 of 10 (Total Marks: 1)
    The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
    True
    False

    QUIZ.NO.1(6)

    Question # 1 of 10 (Total Marks: 1)
    The determinant of a _______ matrix is the product of the diagonal elements.
    Diagonal Page No.70
    Upper triangular
    Lower triangular
    Scalar

    Question # 2 of 10 (Total Marks: 1)
    For differences methods we require the set of values.
    True
    False

    Question # 3 of 10 (Total Marks: 1)
    If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.
    True
    False

    Question # 4 of 10 (Total Marks: 1)
    Central difference method seems to be giving a better approximation, however it requires more computations.
    True
    False

    Question # 5 of 10 (Total Marks: 1)
    Iterative algorithms can be more rapid than direct methods.
    True
    False

    Question # 6 of 10 (Total Marks: 1)
    Central Difference method is the finite difference method.
    True
    False

    Question # 1 of 10 (Total Marks: 1)
    Back substitution procedure is used in …
    Select correct option:
    Gaussian Elimination Method
    Jacobi’s method
    Gauss-Seidel method
    None of the given choices

    Question # 7 of 10 (Total Marks: 1)
    The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
    True
    False

    Question # 8 of 10 (Total Marks: 1)
    Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.
    True (Page102)
    False

    Question # 9 of 10 (Total Marks: 1)
    Power method is applicable if the eigen values are ______________.
    realanddistinct (Page102)
    real and equal
    positive and distinct
    negative and distinct

    Question # 10 of 10 (Total Marks: 1)
    Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials.
    Quadratic (Page174)
    Linear
    Cubic
    Quartic

    QUIZ.NO.1(7)

    Question # 1 of 10 (Total Marks: 1)
    .In Simpson’s Rule, we use parabolas to approximating each part of the curve. This proves to be very efficient as compared to Trapezoidal rule.
    True Click here for detail
    False

    Question # 2 of 10 (Total Marks: 1)
    The predictor-corrector method an implicit method. (multi-step methods)
    True (Page 212)
    False

    Question # 3 of 10 (Total Marks: 1)
    Generally, Adams methods are superior if output at many points is needed.
    True
    False

    Question # 4 of 10 (Total Marks: 1)
    The Trapezoidal rule is a numerical method that approximates the value of a.______________.
    Indefinite integral
    Definiteintegral (Page176)
    Improper integral
    Function

    Question # 5 of 10 (Total Marks: 1)
    The need of numerical integration arises for evaluating the definite integral of a function that has no
    explicit ____________ or whose anti derivative is not easy to obtain.
    Antiderivative
    Derivatives.

    Question # 6 of 10 (Total Marks: 1)
    An indefinite integral may _________ in the sense that the limit defining it may not exist.
    diverge
    Converge

    Question # 7 of 10 (Total Marks: 1)
    An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or -∞ or, in some cases, as both endpoints approach limits.
    TRUE Click here for detail
    FALSE
    Question # 8 of 10 (Total Marks: 1)
    Euler’s Method numerically computes the approximate derivative of a function.
    TRUE
    FALSE
    Question # 9 of 10 (Total Marks: 1)
    Euler’s Method numerically computes the approximate ________ of a function.
    Antiderivative
    Derivative
    Error
    Value
    Question # 10 of 10 (Total Marks: 1)
    If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the
    infinite limit with a variable, and then take the limit as this variable goes to _________.
    Chose the correct option :
    Constant
    Finite
    Infinity Click here for detail
    Zero

    QUIZ.NO.1(8)

    Question # 1 of 10 (Total Marks: 1)
    The Jacobi iteration ______, if A is strictly diagonally dominant.
    converges
    Diverges
    Question # 2 of 10 (Total Marks: 1)
    By using determinants, we can easily check that the solution of the given system of linear equation exits
    and it is unique.
    TRUE
    FALSE
    Question # 3 of 10 (Total Marks: 1)
    The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of

    13

    matrix A
    TRUE
    FALSE
    Question # 4 of 10 (Total Marks: 1)
    Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.
    TRUE
    FALSE
    Question # 5 of 10 (Total Marks: 1)
    Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero
    vector v such that _______.
    Av = xv
    Ax=xv
    Av + xv=0
    Av = Ax1
    Av = λv
    Question # 6 of 10 (Total Marks: 1)
    In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
    Slow Click here for detail
    Fast
    Question # 7 of 10 (Total Marks: 1)
    Numerical solution of 2/3 up to four decimal places is ________.
    0.667
    0.6666
    0.6667
    0.666671.
    Question # 8 of 10 (Total Marks: 1)
    Symbol used for forward differences is
    ∆ (Page 12)
    δ
    μ
    Question # 9 of 10 (Total Marks: 1)
    The relationship between central difference operator and the shift operator is given by
    δ =Ε−Ε-1
    δ = Ε+Ε-1
    δ = Ε1/2+Ε1/2
    δ = E1/2 −Ε1/2
    1 1
    E E 2 2 
    
     

    (Page 152)
    Question # 10 of 10 (Total Marks: 1)

    14

    Muller’s method requires --------starting points
    1
    2
    3 (Page 41)

    QUIZ.NO.1(9)

    Question # 1 of 10 (Total Marks: 1)
    By using determinants, we can easily check that the solution of the given system of linear equation
    ______ and it is ______.
    Select correct option:
    exits, unique
    exists, consistent
    trivial, unique
    nontrivial, inconsistent
    Question # 2 of 10 (Total Marks: 1)
    Two matrices with the _______ characteristic polynomial need not be similar.
    Select correct option:
    same
    different
    Question # 3 of 10 (Total Marks: 1)
    In … method, the elements above and below the diagonal are simultaneously made zero.
    Select correct option:
    Jacobi’s
    Gauss-Seidel
    Gauss–Jordon Elimination (Page 59)
    Relaxation
    Question # 4 of 10 (Total Marks: 1)
    Which of the following is equivalent form of the system of equations in matrix form; AX=B ?
    Select correct option:
    XA = B
    X = B(Inverse of A)
    X =(Inverse of A)B
    BX = A
    Question # 5 of 10 (Total Marks: 1)
    If the determinant of a matrix A is not equal to zero then the system of equations will have…
    Select correct option:
    a unique solution
    many solutions
    infinite many solutions

    15

    None of the given choices
    Question # 6 of 10 (Total Marks: 1)
    Sparse matrix is a matrix with …
    Select correct option:
    Some elements are zero
    Many elements are zero (page 69)
    Some elements are one
    Many elements are one

    MTH603 – 2

    ND QUIZ FILE (24-11-2011)

    EDIT BY MUHAMMAD AWAIS AND MUHAMMAD MOAAZ SIDDIQ

    QUIZ.NO.2(1)
    Question # 1 of 10 ( Start time: 11:18:07 PM ) Total Marks: 1
    How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
    operator is of differentiation?
    Select correct option:
    Infinite many
    Finite Multiple
    None
    Question # 2 of 10 ( Start time: 11:19:00 PM ) Total Marks: 1
    Which of the following rearrangement make strictly diagonal dominant, the system of linear
    equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?
    Select correct option:
    5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1
    –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9
    5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2
    No need to rearrange as system is already in diagonal dominant form.
    Question # 3 of 10 ( Start time: 11:22:12 PM ) Total Marks: 1
    Which of the following is the meaning of partial pivoting while employing the row transformations?
    Select correct option:
    Making the largest element as pivot (Page 50)
    Making the smallest element as pivot
    Making any element as pivot
    Making zero elements as pivot

    16

    Question # 4 of 10 ( Start time: 11:53:06 PM ) Total Marks: 1
    Differences methods are iterative methods.
    Select correct option:
    TRUE
    FALSE

    Question # 5 of 10 ( Start time: 11:55:28 PM ) Total Marks: 1
    Eigenvalues of a _________ matrix are all real.
    Select correct option:
    symmetric
    antisymmetric
    rectangular
    triangular
    Question # 6 of 10 ( Start time: 11:32:38 PM ) Total Marks: 1
    If a system of equations has a property that each of the equation possesses one large coefficient and
    the larger coefficients in the equations correspond to different unknowns in different equations,
    then which of the following iterative method id preferred to apply?
    Select correct option:
    Gauss-Seidel method
    Gauss-Jordon method
    Gauss elimination method
    Crout’s method
    Question # 7 of 10 ( Start time: 11:35:30 PM ) Total Marks: 1
    For a system of linear equations, the corresponding coefficient matrix has the value of determinant;
    |A| = 0, then which of the following is true?
    Select correct option:
    The system has unique solution
    The system has finite multiple solutions
    The system has infinite may solutions
    The system has no solution (Page 48)
    Question # 8 of 10 ( Start time: 11:36:21 PM ) Total Marks: 1
    For the system; 2x+3y = 1, 3x +2y = - 4, if the iterative solution is (0,0) and ‘dxi = 2’ is the increment
    in ‘y’ then which of the following will be taken as next iterative solution?
    Select correct option:
    (2,0)
    (0,3)
    (0,2)
    (1,-4)

    17

    Question # 9 of 10 ( Start time: 11:37:49 PM ) Total Marks: 1
    While using Relaxation method, which of the following is increment ‘dxi’corresponding to the
    largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?
    Select correct option:
    -2
    2
    3
    4
    Question # 10 of 10 ( Start time: 11:40:42 PM)Total Marks: 1
    If system of equations is inconsistent then its means that it has …
    Select correct option:
    No Solutions
    Many solutions
    Infinite Many solutions
    None of the given choices

    QUIZ.NO.2(2)
    Question # 1 of 10 ( Start time: 11:47:15 PM)Total Marks: 1
    Relaxation Method is a/an …
    Select correct option:
    Direct method
    Iterative method
    Question # 2 of 10 ( Start time: 11:33:36 PM ) Total Marks: 1
    How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
    operator is of differentiation?
    Select correct option:
    Finite Multiple
    Infinite many
    Unique
    None

    Question # 3 of 10 ( Start time: 11:36:46 PM ) Total Marks: 1
    The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the
    matrix, remain … to the original vector.
    Select correct option:
    Perpendicular
    Parallel
    Diagonal

    18

    None of the given choices
    Question # 4 of 10 ( Start time: 11:38:16 PM ) Total Marks: 1
    In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be … to
    the sum of the diagonal elements of the original matrix A.
    Select correct option:
    Greater than
    Less than
    Same (Page 106)
    Different
    Question # 5 of 10 (Total Marks: 1)
    In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric
    matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then
    which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?
    Select correct option:
    Pi/3
    Pi/6
    Pi/2
    Pi/4
    Question # 6 of 10 (Total Marks: 1)
    If f (x) contains trigonometric, exponential or logarithmic functions then this equation is known as
    Transcendental Equation (Page 6)
    Algebraic
    Polynomial
    Linear
    Question # 7 of 10 (Total Marks: 1)
    In interpolation is used to represent the d
    Forward difference ?
    Central difference
    Backward difference
    Question # 8 of 10 (Total Marks: 1)
    The Power method can be used only to find the eigen value of A that is largest in absolute value we call
    this eigen value the dominant eigen value of A.
    True
    False
    Question # 9 of 10 (Total Marks: 1)
    Power method is applicable if the eigen vectors corresponding to eigen values are linearly ----.
    Select correct option:
    independent
    dependent

    cyberianC Offline
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    Cyberian's Cyberian's Gold
    wrote on last edited by
    #36

    @zareen said in MTH603 Mid Term Past and Current Solved Paper Discussion:

    Question # 4 of 10 (Total Marks: 1)
    Which of the following is equivalent form of the system of equations in matrix form; AX=B ?
    Select correct option:
    XA = B
    X = B(Inverse of A)
    X =(Inverse of A)B
    BX = A

    The correct answer is:

    X =(Inverse of A)B

    The system of equations in matrix form AX = B is equivalent to X = A^(-1)B, where A^(-1) is the inverse of matrix A. This is because multiplying both sides of the original equation AX = B by A^(-1) yields X = A^(-1)B.

    Discussion is right way to get Solution of the every assignment, Quiz and GDB.
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    • zareenZ zareen

      Question # 1 of 10 (Total Marks: 1)
      While solving a system of linear equations, which of the following approach is economical for the computer memory?
      Select correct option:
      Direct
      Iterative (Page 69)
      Analytical
      Graphical

      Question # 2 of 10 (Total Marks: 1)
      The basic idea of relaxation method is to reduce the largest residual to …
      Select correct option:
      One
      Two
      Zero (Page 83)
      None of the given choices

      Question # 3 of 10 (Total Marks: 1)
      The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its
      ________.
      Select correct option:
      main diagonal (Page 104)
      last column
      last row
      first row

      Question # 4 of 10 (Total Marks: 1)
      If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix ,
      the eigenvalues of A are the diagonal entries of A.
      Select correct option:
      TRUE Click here for detail
      FALSE

      Question # 5 of 10 (Total Marks: 1)
      A 3 x 3 identity matrix have three and different eigen values.
      Select correct option:
      TRUE Click here for detail
      FALSE

      Question # 6 of 10 (Total Marks: 1)
      Which of the following is a reason due to which the LU decomposition of the system of linear equations;
      x+y = 1, x+y =2 is not possible?
      Select correct option:
      Associated coefficient matrix is singular
      All values of l’s and u’s can’t be evaluated
      Determinant of coefficient matrix is zero
      All are equivalent

      Question # 7 of 10 (Total Marks: 1)
      Gauss - Jordan Method is similar to …
      Select correct option:
      Gauss–Seidel method
      Iteration’s method
      Relaxation Method
      Gaussian elimination method (Page 95)

      Question # 8 of 10 (Total Marks: 1)
      While using Relaxation method, which of the following is the largest Residual for 1st iteration on the
      system; 2x+3y = 1, 3x +2y = - 4 ?
      Select correct option:
      -4
      3
      2
      1

      Question # 9 of 10 (Total Marks: 1)
      Gauss–Seidel method is also known as method of …
      Select correct option:
      Successive displacement (Page 263)
      Iterations
      False position
      None of the given choices

      Question # 10 of 10 (Total Marks: 1)
      Jacobi’s Method is a/an…
      Select correct option:
      Iterative method (Page 69)
      Direct method

      QUIZ.NO.1(2)

      Question # 1 of 10 (Total Marks: 1)
      The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the
      given 3 x 3 identity matrix. where symbol ^ shows power.
      Select correct option:
      (x-1)^3
      (x+1)^3
      x^3-1
      x^3+1

      Question # 2 of 10 (Total Marks: 1)
      The can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue
      the dominant eigenvalue of A.
      Select correct option:
      TRUE
      FALSE

      Question # 3 of 10 (Total Marks: 1)
      In … method, a system is reduced to an equivalent diagonal form using elementary
      transformations.
      Select correct option:
      Jacobi’s
      Gauss-Seidel
      Relaxation
      Gaussian elimination (Page 262)

      Question # 4 of 10 (Total Marks: 1)
      The linear equation: 2x+0y-2=0 has -------- solution/solutions.
      Select correct option:
      Unique (Page 48)
      no solution
      infinite many
      finite many

      Question # 5 of 10 (Total Marks: 1)
      Under elimination methods, we consider, Gaussian elimination and …methods.
      Select correct option:
      Gauss-Seidel
      Jacobi
      Gauss-Jordan elimination (Page 48)
      None of the given choices

      Question # 6 of 10 (Total Marks: 1)
      Which of the following method is not an iterative method?
      Select correct option:
      Jacobi’s method
      Gauss-Seidel method
      Relaxation methods
      Gauss-Jordan elimination method

      Question # 7 of 10 (Total Marks: 1)
      An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal
      to zero.
      Select correct option:
      TRUE
      FALSE (Page 97)

      Question # 8 of 10 (Total Marks: 1)
      Exact solution of 2/3 is not exists.
      Select correct option:
      TRUE
      FALSE

      Question # 9 of 10 (Total Marks: 1)
      When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the
      method is …
      Select correct option:
      Stable
      Unstable
      Convergent (Page 70)
      Divergent

      Question # 10 of 10 (Total Marks: 1)
      Gauss–Seidel method is similar to …
      Select correct option:
      Iteration’s method
      Regula-Falsi method
      Jacobi’s method
      None of the given choices (Page 263)

      QUIZ.NO.1(3)

      Question # 1 of 10 (Total Marks: 1)
      Sparse matrices arise in computing the numerical solution of …
      Select correct option:
      Ordinary differential equations
      Partial differential equations (Page 69)
      Linear differential equations
      Non-linear differential equations

      Question # 2 of 10 (Total Marks: 1)
      While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the
      system; x-2y =1, x+4y=4 ?
      Select correct option:
      (1, 0.75)
      (0,0)
      (1,0)
      (0,1)

      Question # 3 of 10 (Total Marks: 1)
      While solving a system of linear equations by Gauss Jordon Method, after all the elementary row
      operations if there lefts also zeros on the main diagonal then which of the is true about the system?
      Select correct option:
      System may have unique solutions
      System has no solution
      System may have multiple numbers of finite solutions
      System may have infinite many solutions

      Question # 4 of 10 (Total Marks: 1)
      Numerical methods for finding the solution of the system of equations are classified as direct and
      … methods
      Select correct option:
      Indirect
      Iterative (Page 48)
      Jacobi
      None of the given choices

      Question # 5 of 10 (Total Marks: 1)
      If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st
      iteration will reduce to -------.
      Select correct option:
      zero
      4
      -1
      -1

      Question # 6 of 10 (Total Marks: 1)
      While using Relaxation method, which of the following is the Residuals for 1st iteration on the system;
      2x+3y = 1, 3x +2y =4 ?
      Select correct option:
      (2,3)
      (3,-2)
      (-2,3)
      (1,4)

      0= 1-2x-3y
      0= 4-3x -2y

      Question # 7 of 10 (Total Marks: 1)
      If the order of coefficient matrix corresponding to system of linear equations is 33 then which of the
      following will be the orders of its decomposed matrices; ‘L’ and ‘U’?
      Select correct option:
      Order of ‘L’ = 3      1, Order of ‘U’ = 13
      Order of ‘L’ = 3      2, Order of ‘U’ = 2*3

      Order of ‘L’ = 33, Order of ‘U’ = 33
      Order of ‘L’ = 34, Order of ‘U’ = 43

      Question # 8 of 10 (Total Marks: 1)
      While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering
      is feasible to have good approximate solution?
      Select correct option:
      x+4y = 1, x-2y = 4
      x+2y = 1, x- 4y =4
      x+4y = 4, x–2y = 1
      no need to reordering

      Question # 9 of 10 (Total Marks: 1)
      Full pivoting, in fact, is more …than the partial pivoting.
      Select correct option:
      Easiest
      Complicated (Page 51)
      Question # 10 of 10 (Total Marks: 1)
      For the equation
      11fd5b6d-0b86-453d-83b2-64f970116bbc-image.png the root of the equation lies in the interval…

      ► (1, 3)
      ► (1, 2)
      ► (0, 1)
      ► (1, 2)

      QUIZ.NO.1(4)

      Question # 1 of 10 (Total Marks: 1)
      …lies in the category of iterative method.
      ► Bisection Method
      ► Regula Falsi Method
      ► Secant Method
      ► all of the given choices (Page 8)

      Question # 2 of 10 (Total Marks: 1)
      If n x n matrices A and B are similar, then they have the different eigenvalues (with the same
      multiplicities).
      True
      False

      Question # 3 of 10 (Total Marks: 1)
      The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its
      main diagonal.
      No Click here for detail
      At least one

      Question # 4 of 10 (Total Marks: 1)
      If the root of the given equation lies between a and b, then the first approximation to the root of the equation by bisection method is …
      b751921b-b3f6-45cd-9112-ad988bc16051-image.png

      Question # 5 of 10 (Total Marks: 1)
      To apply Simpson’s 3/8 rule, the number of intervals in the following must be
      ► 10
      ► 11
      ► 12
      ► 13

      Question # 6 of 10 (Total Marks: 1)
      The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite
      matrices A.
      Select correct option:
      Positive Click here for detail
      negative

      Question # 7 of 10 (Total Marks: 1)
      Differences methods find the ________ solution of the system.
      Select correct option:
      numerical
      Analytical

      Question # 8 of 10 (Total Marks: 1)
      To apply Simpson’s 1/3 rule, the number of intervals in the following must be
      ► 2 (Simpson’‘s 1/3 rule must use an even number of elements’)
      ► 3
      ► 5
      ► 7

      Question # 9 of 10 (Total Marks: 1)
      Bisection and false position methods are also known as bracketing method and are always
      Divergent
      Convergent (Page 26)
      .67

      Question # 10 of 10 (Total Marks: 1)
      The Inverse of a matrix can only be found if the matrix is
      Singular
      None Singular: Every square non-singular matrix will have an inverse.
      Scalar
      Diagonal

      QUIZ.NO.1(5)

      Question # 1 of 10 (Total Marks: 1)
      In interpolation is used to represent the δ
      Forward difference Δ
      Central difference (Page 117)
      Backward difference

      Question # 2 of 10 (Total Marks: 1)
      The base of the decimal system is _______
      10
      0
      2
      8
      None of the above.

      Question # 3 of 10 (Total Marks: 1)
      Bisection method is … method
      ► Open Method
      ► Bracketing Method (page 26)

      Question # 4 of 10 (Total Marks: 1)
      A 3 x 3 identity matrix have three and __________eigen values.
      same
      different

      Question # 5 of 10 (Total Marks: 1)
      Eigenvalues of a symmetric matrix are all _______ .
      Real (page 104)
      complex
      zero
      positive

      Question # 6 of 10 (Total Marks: 1)
      The Jacobi iteration converges, if A is strictly diagonally dominant.
      TRUE (Page 69)
      FALSE

      Question # 7 of 10 (Total Marks: 1)
      Below are all the finite difference methods EXCEPT _________.
      jacobi’s method
      newton’s backward difference method
      Stirlling formula
      Forward difference method

      Question # 8 of 10 (Total Marks: 1)
      Two matrices with the same characteristic polynomial need not be similar.
      TRUE
      FALSE

      Question # 9 of 10 (Total Marks: 1) No.69
      The determinant of a diagonal matrix is the product of the diagonal elements.
      True
      False

      Question # 10 of 10 (Total Marks: 1)
      The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
      True
      False

      QUIZ.NO.1(6)

      Question # 1 of 10 (Total Marks: 1)
      The determinant of a _______ matrix is the product of the diagonal elements.
      Diagonal Page No.70
      Upper triangular
      Lower triangular
      Scalar

      Question # 2 of 10 (Total Marks: 1)
      For differences methods we require the set of values.
      True
      False

      Question # 3 of 10 (Total Marks: 1)
      If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.
      True
      False

      Question # 4 of 10 (Total Marks: 1)
      Central difference method seems to be giving a better approximation, however it requires more computations.
      True
      False

      Question # 5 of 10 (Total Marks: 1)
      Iterative algorithms can be more rapid than direct methods.
      True
      False

      Question # 6 of 10 (Total Marks: 1)
      Central Difference method is the finite difference method.
      True
      False

      Question # 1 of 10 (Total Marks: 1)
      Back substitution procedure is used in …
      Select correct option:
      Gaussian Elimination Method
      Jacobi’s method
      Gauss-Seidel method
      None of the given choices

      Question # 7 of 10 (Total Marks: 1)
      The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
      True
      False

      Question # 8 of 10 (Total Marks: 1)
      Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.
      True (Page102)
      False

      Question # 9 of 10 (Total Marks: 1)
      Power method is applicable if the eigen values are ______________.
      realanddistinct (Page102)
      real and equal
      positive and distinct
      negative and distinct

      Question # 10 of 10 (Total Marks: 1)
      Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials.
      Quadratic (Page174)
      Linear
      Cubic
      Quartic

      QUIZ.NO.1(7)

      Question # 1 of 10 (Total Marks: 1)
      .In Simpson’s Rule, we use parabolas to approximating each part of the curve. This proves to be very efficient as compared to Trapezoidal rule.
      True Click here for detail
      False

      Question # 2 of 10 (Total Marks: 1)
      The predictor-corrector method an implicit method. (multi-step methods)
      True (Page 212)
      False

      Question # 3 of 10 (Total Marks: 1)
      Generally, Adams methods are superior if output at many points is needed.
      True
      False

      Question # 4 of 10 (Total Marks: 1)
      The Trapezoidal rule is a numerical method that approximates the value of a.______________.
      Indefinite integral
      Definiteintegral (Page176)
      Improper integral
      Function

      Question # 5 of 10 (Total Marks: 1)
      The need of numerical integration arises for evaluating the definite integral of a function that has no
      explicit ____________ or whose anti derivative is not easy to obtain.
      Antiderivative
      Derivatives.

      Question # 6 of 10 (Total Marks: 1)
      An indefinite integral may _________ in the sense that the limit defining it may not exist.
      diverge
      Converge

      Question # 7 of 10 (Total Marks: 1)
      An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or -∞ or, in some cases, as both endpoints approach limits.
      TRUE Click here for detail
      FALSE
      Question # 8 of 10 (Total Marks: 1)
      Euler’s Method numerically computes the approximate derivative of a function.
      TRUE
      FALSE
      Question # 9 of 10 (Total Marks: 1)
      Euler’s Method numerically computes the approximate ________ of a function.
      Antiderivative
      Derivative
      Error
      Value
      Question # 10 of 10 (Total Marks: 1)
      If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the
      infinite limit with a variable, and then take the limit as this variable goes to _________.
      Chose the correct option :
      Constant
      Finite
      Infinity Click here for detail
      Zero

      QUIZ.NO.1(8)

      Question # 1 of 10 (Total Marks: 1)
      The Jacobi iteration ______, if A is strictly diagonally dominant.
      converges
      Diverges
      Question # 2 of 10 (Total Marks: 1)
      By using determinants, we can easily check that the solution of the given system of linear equation exits
      and it is unique.
      TRUE
      FALSE
      Question # 3 of 10 (Total Marks: 1)
      The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of

      13

      matrix A
      TRUE
      FALSE
      Question # 4 of 10 (Total Marks: 1)
      Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.
      TRUE
      FALSE
      Question # 5 of 10 (Total Marks: 1)
      Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero
      vector v such that _______.
      Av = xv
      Ax=xv
      Av + xv=0
      Av = Ax1
      Av = λv
      Question # 6 of 10 (Total Marks: 1)
      In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
      Slow Click here for detail
      Fast
      Question # 7 of 10 (Total Marks: 1)
      Numerical solution of 2/3 up to four decimal places is ________.
      0.667
      0.6666
      0.6667
      0.666671.
      Question # 8 of 10 (Total Marks: 1)
      Symbol used for forward differences is
      ∆ (Page 12)
      δ
      μ
      Question # 9 of 10 (Total Marks: 1)
      The relationship between central difference operator and the shift operator is given by
      δ =Ε−Ε-1
      δ = Ε+Ε-1
      δ = Ε1/2+Ε1/2
      δ = E1/2 −Ε1/2
      1 1
      E E 2 2 
      
       

      (Page 152)
      Question # 10 of 10 (Total Marks: 1)

      14

      Muller’s method requires --------starting points
      1
      2
      3 (Page 41)

      QUIZ.NO.1(9)

      Question # 1 of 10 (Total Marks: 1)
      By using determinants, we can easily check that the solution of the given system of linear equation
      ______ and it is ______.
      Select correct option:
      exits, unique
      exists, consistent
      trivial, unique
      nontrivial, inconsistent
      Question # 2 of 10 (Total Marks: 1)
      Two matrices with the _______ characteristic polynomial need not be similar.
      Select correct option:
      same
      different
      Question # 3 of 10 (Total Marks: 1)
      In … method, the elements above and below the diagonal are simultaneously made zero.
      Select correct option:
      Jacobi’s
      Gauss-Seidel
      Gauss–Jordon Elimination (Page 59)
      Relaxation
      Question # 4 of 10 (Total Marks: 1)
      Which of the following is equivalent form of the system of equations in matrix form; AX=B ?
      Select correct option:
      XA = B
      X = B(Inverse of A)
      X =(Inverse of A)B
      BX = A
      Question # 5 of 10 (Total Marks: 1)
      If the determinant of a matrix A is not equal to zero then the system of equations will have…
      Select correct option:
      a unique solution
      many solutions
      infinite many solutions

      15

      None of the given choices
      Question # 6 of 10 (Total Marks: 1)
      Sparse matrix is a matrix with …
      Select correct option:
      Some elements are zero
      Many elements are zero (page 69)
      Some elements are one
      Many elements are one

      MTH603 – 2

      ND QUIZ FILE (24-11-2011)

      EDIT BY MUHAMMAD AWAIS AND MUHAMMAD MOAAZ SIDDIQ

      QUIZ.NO.2(1)
      Question # 1 of 10 ( Start time: 11:18:07 PM ) Total Marks: 1
      How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
      operator is of differentiation?
      Select correct option:
      Infinite many
      Finite Multiple
      None
      Question # 2 of 10 ( Start time: 11:19:00 PM ) Total Marks: 1
      Which of the following rearrangement make strictly diagonal dominant, the system of linear
      equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?
      Select correct option:
      5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1
      –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9
      5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2
      No need to rearrange as system is already in diagonal dominant form.
      Question # 3 of 10 ( Start time: 11:22:12 PM ) Total Marks: 1
      Which of the following is the meaning of partial pivoting while employing the row transformations?
      Select correct option:
      Making the largest element as pivot (Page 50)
      Making the smallest element as pivot
      Making any element as pivot
      Making zero elements as pivot

      16

      Question # 4 of 10 ( Start time: 11:53:06 PM ) Total Marks: 1
      Differences methods are iterative methods.
      Select correct option:
      TRUE
      FALSE

      Question # 5 of 10 ( Start time: 11:55:28 PM ) Total Marks: 1
      Eigenvalues of a _________ matrix are all real.
      Select correct option:
      symmetric
      antisymmetric
      rectangular
      triangular
      Question # 6 of 10 ( Start time: 11:32:38 PM ) Total Marks: 1
      If a system of equations has a property that each of the equation possesses one large coefficient and
      the larger coefficients in the equations correspond to different unknowns in different equations,
      then which of the following iterative method id preferred to apply?
      Select correct option:
      Gauss-Seidel method
      Gauss-Jordon method
      Gauss elimination method
      Crout’s method
      Question # 7 of 10 ( Start time: 11:35:30 PM ) Total Marks: 1
      For a system of linear equations, the corresponding coefficient matrix has the value of determinant;
      |A| = 0, then which of the following is true?
      Select correct option:
      The system has unique solution
      The system has finite multiple solutions
      The system has infinite may solutions
      The system has no solution (Page 48)
      Question # 8 of 10 ( Start time: 11:36:21 PM ) Total Marks: 1
      For the system; 2x+3y = 1, 3x +2y = - 4, if the iterative solution is (0,0) and ‘dxi = 2’ is the increment
      in ‘y’ then which of the following will be taken as next iterative solution?
      Select correct option:
      (2,0)
      (0,3)
      (0,2)
      (1,-4)

      17

      Question # 9 of 10 ( Start time: 11:37:49 PM ) Total Marks: 1
      While using Relaxation method, which of the following is increment ‘dxi’corresponding to the
      largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?
      Select correct option:
      -2
      2
      3
      4
      Question # 10 of 10 ( Start time: 11:40:42 PM)Total Marks: 1
      If system of equations is inconsistent then its means that it has …
      Select correct option:
      No Solutions
      Many solutions
      Infinite Many solutions
      None of the given choices

      QUIZ.NO.2(2)
      Question # 1 of 10 ( Start time: 11:47:15 PM)Total Marks: 1
      Relaxation Method is a/an …
      Select correct option:
      Direct method
      Iterative method
      Question # 2 of 10 ( Start time: 11:33:36 PM ) Total Marks: 1
      How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
      operator is of differentiation?
      Select correct option:
      Finite Multiple
      Infinite many
      Unique
      None

      Question # 3 of 10 ( Start time: 11:36:46 PM ) Total Marks: 1
      The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the
      matrix, remain … to the original vector.
      Select correct option:
      Perpendicular
      Parallel
      Diagonal

      18

      None of the given choices
      Question # 4 of 10 ( Start time: 11:38:16 PM ) Total Marks: 1
      In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be … to
      the sum of the diagonal elements of the original matrix A.
      Select correct option:
      Greater than
      Less than
      Same (Page 106)
      Different
      Question # 5 of 10 (Total Marks: 1)
      In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric
      matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then
      which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?
      Select correct option:
      Pi/3
      Pi/6
      Pi/2
      Pi/4
      Question # 6 of 10 (Total Marks: 1)
      If f (x) contains trigonometric, exponential or logarithmic functions then this equation is known as
      Transcendental Equation (Page 6)
      Algebraic
      Polynomial
      Linear
      Question # 7 of 10 (Total Marks: 1)
      In interpolation is used to represent the d
      Forward difference ?
      Central difference
      Backward difference
      Question # 8 of 10 (Total Marks: 1)
      The Power method can be used only to find the eigen value of A that is largest in absolute value we call
      this eigen value the dominant eigen value of A.
      True
      False
      Question # 9 of 10 (Total Marks: 1)
      Power method is applicable if the eigen vectors corresponding to eigen values are linearly ----.
      Select correct option:
      independent
      dependent

      cyberianC Offline
      cyberianC Offline
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      Cyberian's Cyberian's Gold
      wrote on last edited by
      #37

      @zareen said in MTH603 Mid Term Past and Current Solved Paper Discussion:

      Question # 5 of 10 (Total Marks: 1)
      If the determinant of a matrix A is not equal to zero then the system of equations will have…
      Select correct option:
      a unique solution
      many solutions
      infinite many solutions

      15

      None of the given choices

      The correct answer is:

      a unique solution

      If the determinant of a matrix A is not equal to zero, then the system of equations represented by AX = B will have a unique solution. This is because a non-zero determinant indicates that the matrix A is invertible, and therefore the system of equations has a unique solution.

      Discussion is right way to get Solution of the every assignment, Quiz and GDB.
      We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
      Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
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      • zareenZ zareen

        Question # 1 of 10 (Total Marks: 1)
        While solving a system of linear equations, which of the following approach is economical for the computer memory?
        Select correct option:
        Direct
        Iterative (Page 69)
        Analytical
        Graphical

        Question # 2 of 10 (Total Marks: 1)
        The basic idea of relaxation method is to reduce the largest residual to …
        Select correct option:
        One
        Two
        Zero (Page 83)
        None of the given choices

        Question # 3 of 10 (Total Marks: 1)
        The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its
        ________.
        Select correct option:
        main diagonal (Page 104)
        last column
        last row
        first row

        Question # 4 of 10 (Total Marks: 1)
        If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix ,
        the eigenvalues of A are the diagonal entries of A.
        Select correct option:
        TRUE Click here for detail
        FALSE

        Question # 5 of 10 (Total Marks: 1)
        A 3 x 3 identity matrix have three and different eigen values.
        Select correct option:
        TRUE Click here for detail
        FALSE

        Question # 6 of 10 (Total Marks: 1)
        Which of the following is a reason due to which the LU decomposition of the system of linear equations;
        x+y = 1, x+y =2 is not possible?
        Select correct option:
        Associated coefficient matrix is singular
        All values of l’s and u’s can’t be evaluated
        Determinant of coefficient matrix is zero
        All are equivalent

        Question # 7 of 10 (Total Marks: 1)
        Gauss - Jordan Method is similar to …
        Select correct option:
        Gauss–Seidel method
        Iteration’s method
        Relaxation Method
        Gaussian elimination method (Page 95)

        Question # 8 of 10 (Total Marks: 1)
        While using Relaxation method, which of the following is the largest Residual for 1st iteration on the
        system; 2x+3y = 1, 3x +2y = - 4 ?
        Select correct option:
        -4
        3
        2
        1

        Question # 9 of 10 (Total Marks: 1)
        Gauss–Seidel method is also known as method of …
        Select correct option:
        Successive displacement (Page 263)
        Iterations
        False position
        None of the given choices

        Question # 10 of 10 (Total Marks: 1)
        Jacobi’s Method is a/an…
        Select correct option:
        Iterative method (Page 69)
        Direct method

        QUIZ.NO.1(2)

        Question # 1 of 10 (Total Marks: 1)
        The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the
        given 3 x 3 identity matrix. where symbol ^ shows power.
        Select correct option:
        (x-1)^3
        (x+1)^3
        x^3-1
        x^3+1

        Question # 2 of 10 (Total Marks: 1)
        The can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue
        the dominant eigenvalue of A.
        Select correct option:
        TRUE
        FALSE

        Question # 3 of 10 (Total Marks: 1)
        In … method, a system is reduced to an equivalent diagonal form using elementary
        transformations.
        Select correct option:
        Jacobi’s
        Gauss-Seidel
        Relaxation
        Gaussian elimination (Page 262)

        Question # 4 of 10 (Total Marks: 1)
        The linear equation: 2x+0y-2=0 has -------- solution/solutions.
        Select correct option:
        Unique (Page 48)
        no solution
        infinite many
        finite many

        Question # 5 of 10 (Total Marks: 1)
        Under elimination methods, we consider, Gaussian elimination and …methods.
        Select correct option:
        Gauss-Seidel
        Jacobi
        Gauss-Jordan elimination (Page 48)
        None of the given choices

        Question # 6 of 10 (Total Marks: 1)
        Which of the following method is not an iterative method?
        Select correct option:
        Jacobi’s method
        Gauss-Seidel method
        Relaxation methods
        Gauss-Jordan elimination method

        Question # 7 of 10 (Total Marks: 1)
        An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal
        to zero.
        Select correct option:
        TRUE
        FALSE (Page 97)

        Question # 8 of 10 (Total Marks: 1)
        Exact solution of 2/3 is not exists.
        Select correct option:
        TRUE
        FALSE

        Question # 9 of 10 (Total Marks: 1)
        When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the
        method is …
        Select correct option:
        Stable
        Unstable
        Convergent (Page 70)
        Divergent

        Question # 10 of 10 (Total Marks: 1)
        Gauss–Seidel method is similar to …
        Select correct option:
        Iteration’s method
        Regula-Falsi method
        Jacobi’s method
        None of the given choices (Page 263)

        QUIZ.NO.1(3)

        Question # 1 of 10 (Total Marks: 1)
        Sparse matrices arise in computing the numerical solution of …
        Select correct option:
        Ordinary differential equations
        Partial differential equations (Page 69)
        Linear differential equations
        Non-linear differential equations

        Question # 2 of 10 (Total Marks: 1)
        While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the
        system; x-2y =1, x+4y=4 ?
        Select correct option:
        (1, 0.75)
        (0,0)
        (1,0)
        (0,1)

        Question # 3 of 10 (Total Marks: 1)
        While solving a system of linear equations by Gauss Jordon Method, after all the elementary row
        operations if there lefts also zeros on the main diagonal then which of the is true about the system?
        Select correct option:
        System may have unique solutions
        System has no solution
        System may have multiple numbers of finite solutions
        System may have infinite many solutions

        Question # 4 of 10 (Total Marks: 1)
        Numerical methods for finding the solution of the system of equations are classified as direct and
        … methods
        Select correct option:
        Indirect
        Iterative (Page 48)
        Jacobi
        None of the given choices

        Question # 5 of 10 (Total Marks: 1)
        If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st
        iteration will reduce to -------.
        Select correct option:
        zero
        4
        -1
        -1

        Question # 6 of 10 (Total Marks: 1)
        While using Relaxation method, which of the following is the Residuals for 1st iteration on the system;
        2x+3y = 1, 3x +2y =4 ?
        Select correct option:
        (2,3)
        (3,-2)
        (-2,3)
        (1,4)

        0= 1-2x-3y
        0= 4-3x -2y

        Question # 7 of 10 (Total Marks: 1)
        If the order of coefficient matrix corresponding to system of linear equations is 33 then which of the
        following will be the orders of its decomposed matrices; ‘L’ and ‘U’?
        Select correct option:
        Order of ‘L’ = 3        1, Order of ‘U’ = 13
        Order of ‘L’ = 3        2, Order of ‘U’ = 2*3

        Order of ‘L’ = 33, Order of ‘U’ = 33
        Order of ‘L’ = 34, Order of ‘U’ = 43

        Question # 8 of 10 (Total Marks: 1)
        While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering
        is feasible to have good approximate solution?
        Select correct option:
        x+4y = 1, x-2y = 4
        x+2y = 1, x- 4y =4
        x+4y = 4, x–2y = 1
        no need to reordering

        Question # 9 of 10 (Total Marks: 1)
        Full pivoting, in fact, is more …than the partial pivoting.
        Select correct option:
        Easiest
        Complicated (Page 51)
        Question # 10 of 10 (Total Marks: 1)
        For the equation
        11fd5b6d-0b86-453d-83b2-64f970116bbc-image.png the root of the equation lies in the interval…

        ► (1, 3)
        ► (1, 2)
        ► (0, 1)
        ► (1, 2)

        QUIZ.NO.1(4)

        Question # 1 of 10 (Total Marks: 1)
        …lies in the category of iterative method.
        ► Bisection Method
        ► Regula Falsi Method
        ► Secant Method
        ► all of the given choices (Page 8)

        Question # 2 of 10 (Total Marks: 1)
        If n x n matrices A and B are similar, then they have the different eigenvalues (with the same
        multiplicities).
        True
        False

        Question # 3 of 10 (Total Marks: 1)
        The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its
        main diagonal.
        No Click here for detail
        At least one

        Question # 4 of 10 (Total Marks: 1)
        If the root of the given equation lies between a and b, then the first approximation to the root of the equation by bisection method is …
        b751921b-b3f6-45cd-9112-ad988bc16051-image.png

        Question # 5 of 10 (Total Marks: 1)
        To apply Simpson’s 3/8 rule, the number of intervals in the following must be
        ► 10
        ► 11
        ► 12
        ► 13

        Question # 6 of 10 (Total Marks: 1)
        The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite
        matrices A.
        Select correct option:
        Positive Click here for detail
        negative

        Question # 7 of 10 (Total Marks: 1)
        Differences methods find the ________ solution of the system.
        Select correct option:
        numerical
        Analytical

        Question # 8 of 10 (Total Marks: 1)
        To apply Simpson’s 1/3 rule, the number of intervals in the following must be
        ► 2 (Simpson’‘s 1/3 rule must use an even number of elements’)
        ► 3
        ► 5
        ► 7

        Question # 9 of 10 (Total Marks: 1)
        Bisection and false position methods are also known as bracketing method and are always
        Divergent
        Convergent (Page 26)
        .67

        Question # 10 of 10 (Total Marks: 1)
        The Inverse of a matrix can only be found if the matrix is
        Singular
        None Singular: Every square non-singular matrix will have an inverse.
        Scalar
        Diagonal

        QUIZ.NO.1(5)

        Question # 1 of 10 (Total Marks: 1)
        In interpolation is used to represent the δ
        Forward difference Δ
        Central difference (Page 117)
        Backward difference

        Question # 2 of 10 (Total Marks: 1)
        The base of the decimal system is _______
        10
        0
        2
        8
        None of the above.

        Question # 3 of 10 (Total Marks: 1)
        Bisection method is … method
        ► Open Method
        ► Bracketing Method (page 26)

        Question # 4 of 10 (Total Marks: 1)
        A 3 x 3 identity matrix have three and __________eigen values.
        same
        different

        Question # 5 of 10 (Total Marks: 1)
        Eigenvalues of a symmetric matrix are all _______ .
        Real (page 104)
        complex
        zero
        positive

        Question # 6 of 10 (Total Marks: 1)
        The Jacobi iteration converges, if A is strictly diagonally dominant.
        TRUE (Page 69)
        FALSE

        Question # 7 of 10 (Total Marks: 1)
        Below are all the finite difference methods EXCEPT _________.
        jacobi’s method
        newton’s backward difference method
        Stirlling formula
        Forward difference method

        Question # 8 of 10 (Total Marks: 1)
        Two matrices with the same characteristic polynomial need not be similar.
        TRUE
        FALSE

        Question # 9 of 10 (Total Marks: 1) No.69
        The determinant of a diagonal matrix is the product of the diagonal elements.
        True
        False

        Question # 10 of 10 (Total Marks: 1)
        The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
        True
        False

        QUIZ.NO.1(6)

        Question # 1 of 10 (Total Marks: 1)
        The determinant of a _______ matrix is the product of the diagonal elements.
        Diagonal Page No.70
        Upper triangular
        Lower triangular
        Scalar

        Question # 2 of 10 (Total Marks: 1)
        For differences methods we require the set of values.
        True
        False

        Question # 3 of 10 (Total Marks: 1)
        If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.
        True
        False

        Question # 4 of 10 (Total Marks: 1)
        Central difference method seems to be giving a better approximation, however it requires more computations.
        True
        False

        Question # 5 of 10 (Total Marks: 1)
        Iterative algorithms can be more rapid than direct methods.
        True
        False

        Question # 6 of 10 (Total Marks: 1)
        Central Difference method is the finite difference method.
        True
        False

        Question # 1 of 10 (Total Marks: 1)
        Back substitution procedure is used in …
        Select correct option:
        Gaussian Elimination Method
        Jacobi’s method
        Gauss-Seidel method
        None of the given choices

        Question # 7 of 10 (Total Marks: 1)
        The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
        True
        False

        Question # 8 of 10 (Total Marks: 1)
        Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.
        True (Page102)
        False

        Question # 9 of 10 (Total Marks: 1)
        Power method is applicable if the eigen values are ______________.
        realanddistinct (Page102)
        real and equal
        positive and distinct
        negative and distinct

        Question # 10 of 10 (Total Marks: 1)
        Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials.
        Quadratic (Page174)
        Linear
        Cubic
        Quartic

        QUIZ.NO.1(7)

        Question # 1 of 10 (Total Marks: 1)
        .In Simpson’s Rule, we use parabolas to approximating each part of the curve. This proves to be very efficient as compared to Trapezoidal rule.
        True Click here for detail
        False

        Question # 2 of 10 (Total Marks: 1)
        The predictor-corrector method an implicit method. (multi-step methods)
        True (Page 212)
        False

        Question # 3 of 10 (Total Marks: 1)
        Generally, Adams methods are superior if output at many points is needed.
        True
        False

        Question # 4 of 10 (Total Marks: 1)
        The Trapezoidal rule is a numerical method that approximates the value of a.______________.
        Indefinite integral
        Definiteintegral (Page176)
        Improper integral
        Function

        Question # 5 of 10 (Total Marks: 1)
        The need of numerical integration arises for evaluating the definite integral of a function that has no
        explicit ____________ or whose anti derivative is not easy to obtain.
        Antiderivative
        Derivatives.

        Question # 6 of 10 (Total Marks: 1)
        An indefinite integral may _________ in the sense that the limit defining it may not exist.
        diverge
        Converge

        Question # 7 of 10 (Total Marks: 1)
        An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or -∞ or, in some cases, as both endpoints approach limits.
        TRUE Click here for detail
        FALSE
        Question # 8 of 10 (Total Marks: 1)
        Euler’s Method numerically computes the approximate derivative of a function.
        TRUE
        FALSE
        Question # 9 of 10 (Total Marks: 1)
        Euler’s Method numerically computes the approximate ________ of a function.
        Antiderivative
        Derivative
        Error
        Value
        Question # 10 of 10 (Total Marks: 1)
        If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the
        infinite limit with a variable, and then take the limit as this variable goes to _________.
        Chose the correct option :
        Constant
        Finite
        Infinity Click here for detail
        Zero

        QUIZ.NO.1(8)

        Question # 1 of 10 (Total Marks: 1)
        The Jacobi iteration ______, if A is strictly diagonally dominant.
        converges
        Diverges
        Question # 2 of 10 (Total Marks: 1)
        By using determinants, we can easily check that the solution of the given system of linear equation exits
        and it is unique.
        TRUE
        FALSE
        Question # 3 of 10 (Total Marks: 1)
        The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of

        13

        matrix A
        TRUE
        FALSE
        Question # 4 of 10 (Total Marks: 1)
        Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.
        TRUE
        FALSE
        Question # 5 of 10 (Total Marks: 1)
        Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero
        vector v such that _______.
        Av = xv
        Ax=xv
        Av + xv=0
        Av = Ax1
        Av = λv
        Question # 6 of 10 (Total Marks: 1)
        In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
        Slow Click here for detail
        Fast
        Question # 7 of 10 (Total Marks: 1)
        Numerical solution of 2/3 up to four decimal places is ________.
        0.667
        0.6666
        0.6667
        0.666671.
        Question # 8 of 10 (Total Marks: 1)
        Symbol used for forward differences is
        ∆ (Page 12)
        δ
        μ
        Question # 9 of 10 (Total Marks: 1)
        The relationship between central difference operator and the shift operator is given by
        δ =Ε−Ε-1
        δ = Ε+Ε-1
        δ = Ε1/2+Ε1/2
        δ = E1/2 −Ε1/2
        1 1
        E E 2 2 
        
         

        (Page 152)
        Question # 10 of 10 (Total Marks: 1)

        14

        Muller’s method requires --------starting points
        1
        2
        3 (Page 41)

        QUIZ.NO.1(9)

        Question # 1 of 10 (Total Marks: 1)
        By using determinants, we can easily check that the solution of the given system of linear equation
        ______ and it is ______.
        Select correct option:
        exits, unique
        exists, consistent
        trivial, unique
        nontrivial, inconsistent
        Question # 2 of 10 (Total Marks: 1)
        Two matrices with the _______ characteristic polynomial need not be similar.
        Select correct option:
        same
        different
        Question # 3 of 10 (Total Marks: 1)
        In … method, the elements above and below the diagonal are simultaneously made zero.
        Select correct option:
        Jacobi’s
        Gauss-Seidel
        Gauss–Jordon Elimination (Page 59)
        Relaxation
        Question # 4 of 10 (Total Marks: 1)
        Which of the following is equivalent form of the system of equations in matrix form; AX=B ?
        Select correct option:
        XA = B
        X = B(Inverse of A)
        X =(Inverse of A)B
        BX = A
        Question # 5 of 10 (Total Marks: 1)
        If the determinant of a matrix A is not equal to zero then the system of equations will have…
        Select correct option:
        a unique solution
        many solutions
        infinite many solutions

        15

        None of the given choices
        Question # 6 of 10 (Total Marks: 1)
        Sparse matrix is a matrix with …
        Select correct option:
        Some elements are zero
        Many elements are zero (page 69)
        Some elements are one
        Many elements are one

        MTH603 – 2

        ND QUIZ FILE (24-11-2011)

        EDIT BY MUHAMMAD AWAIS AND MUHAMMAD MOAAZ SIDDIQ

        QUIZ.NO.2(1)
        Question # 1 of 10 ( Start time: 11:18:07 PM ) Total Marks: 1
        How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
        operator is of differentiation?
        Select correct option:
        Infinite many
        Finite Multiple
        None
        Question # 2 of 10 ( Start time: 11:19:00 PM ) Total Marks: 1
        Which of the following rearrangement make strictly diagonal dominant, the system of linear
        equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?
        Select correct option:
        5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1
        –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9
        5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2
        No need to rearrange as system is already in diagonal dominant form.
        Question # 3 of 10 ( Start time: 11:22:12 PM ) Total Marks: 1
        Which of the following is the meaning of partial pivoting while employing the row transformations?
        Select correct option:
        Making the largest element as pivot (Page 50)
        Making the smallest element as pivot
        Making any element as pivot
        Making zero elements as pivot

        16

        Question # 4 of 10 ( Start time: 11:53:06 PM ) Total Marks: 1
        Differences methods are iterative methods.
        Select correct option:
        TRUE
        FALSE

        Question # 5 of 10 ( Start time: 11:55:28 PM ) Total Marks: 1
        Eigenvalues of a _________ matrix are all real.
        Select correct option:
        symmetric
        antisymmetric
        rectangular
        triangular
        Question # 6 of 10 ( Start time: 11:32:38 PM ) Total Marks: 1
        If a system of equations has a property that each of the equation possesses one large coefficient and
        the larger coefficients in the equations correspond to different unknowns in different equations,
        then which of the following iterative method id preferred to apply?
        Select correct option:
        Gauss-Seidel method
        Gauss-Jordon method
        Gauss elimination method
        Crout’s method
        Question # 7 of 10 ( Start time: 11:35:30 PM ) Total Marks: 1
        For a system of linear equations, the corresponding coefficient matrix has the value of determinant;
        |A| = 0, then which of the following is true?
        Select correct option:
        The system has unique solution
        The system has finite multiple solutions
        The system has infinite may solutions
        The system has no solution (Page 48)
        Question # 8 of 10 ( Start time: 11:36:21 PM ) Total Marks: 1
        For the system; 2x+3y = 1, 3x +2y = - 4, if the iterative solution is (0,0) and ‘dxi = 2’ is the increment
        in ‘y’ then which of the following will be taken as next iterative solution?
        Select correct option:
        (2,0)
        (0,3)
        (0,2)
        (1,-4)

        17

        Question # 9 of 10 ( Start time: 11:37:49 PM ) Total Marks: 1
        While using Relaxation method, which of the following is increment ‘dxi’corresponding to the
        largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?
        Select correct option:
        -2
        2
        3
        4
        Question # 10 of 10 ( Start time: 11:40:42 PM)Total Marks: 1
        If system of equations is inconsistent then its means that it has …
        Select correct option:
        No Solutions
        Many solutions
        Infinite Many solutions
        None of the given choices

        QUIZ.NO.2(2)
        Question # 1 of 10 ( Start time: 11:47:15 PM)Total Marks: 1
        Relaxation Method is a/an …
        Select correct option:
        Direct method
        Iterative method
        Question # 2 of 10 ( Start time: 11:33:36 PM ) Total Marks: 1
        How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
        operator is of differentiation?
        Select correct option:
        Finite Multiple
        Infinite many
        Unique
        None

        Question # 3 of 10 ( Start time: 11:36:46 PM ) Total Marks: 1
        The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the
        matrix, remain … to the original vector.
        Select correct option:
        Perpendicular
        Parallel
        Diagonal

        18

        None of the given choices
        Question # 4 of 10 ( Start time: 11:38:16 PM ) Total Marks: 1
        In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be … to
        the sum of the diagonal elements of the original matrix A.
        Select correct option:
        Greater than
        Less than
        Same (Page 106)
        Different
        Question # 5 of 10 (Total Marks: 1)
        In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric
        matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then
        which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?
        Select correct option:
        Pi/3
        Pi/6
        Pi/2
        Pi/4
        Question # 6 of 10 (Total Marks: 1)
        If f (x) contains trigonometric, exponential or logarithmic functions then this equation is known as
        Transcendental Equation (Page 6)
        Algebraic
        Polynomial
        Linear
        Question # 7 of 10 (Total Marks: 1)
        In interpolation is used to represent the d
        Forward difference ?
        Central difference
        Backward difference
        Question # 8 of 10 (Total Marks: 1)
        The Power method can be used only to find the eigen value of A that is largest in absolute value we call
        this eigen value the dominant eigen value of A.
        True
        False
        Question # 9 of 10 (Total Marks: 1)
        Power method is applicable if the eigen vectors corresponding to eigen values are linearly ----.
        Select correct option:
        independent
        dependent

        cyberianC Offline
        cyberianC Offline
        cyberian
        Cyberian's Cyberian's Gold
        wrote on last edited by
        #38

        @zareen said in MTH603 Mid Term Past and Current Solved Paper Discussion:

        Question # 6 of 10 (Total Marks: 1)
        Sparse matrix is a matrix with …
        Select correct option:
        Some elements are zero
        Many elements are zero (page 69)
        Some elements are one
        Many elements are one

        The correct answer is:

        Many elements are zero

        A sparse matrix is a matrix in which many of its elements are zero. This is in contrast to a dense matrix, where most of the elements are non-zero. Sparse matrices are often used to represent systems where many of the interactions or relationships between variables are zero or insignificant.

        Discussion is right way to get Solution of the every assignment, Quiz and GDB.
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        • zareenZ zareen

          Question # 1 of 10 (Total Marks: 1)
          While solving a system of linear equations, which of the following approach is economical for the computer memory?
          Select correct option:
          Direct
          Iterative (Page 69)
          Analytical
          Graphical

          Question # 2 of 10 (Total Marks: 1)
          The basic idea of relaxation method is to reduce the largest residual to …
          Select correct option:
          One
          Two
          Zero (Page 83)
          None of the given choices

          Question # 3 of 10 (Total Marks: 1)
          The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its
          ________.
          Select correct option:
          main diagonal (Page 104)
          last column
          last row
          first row

          Question # 4 of 10 (Total Marks: 1)
          If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix ,
          the eigenvalues of A are the diagonal entries of A.
          Select correct option:
          TRUE Click here for detail
          FALSE

          Question # 5 of 10 (Total Marks: 1)
          A 3 x 3 identity matrix have three and different eigen values.
          Select correct option:
          TRUE Click here for detail
          FALSE

          Question # 6 of 10 (Total Marks: 1)
          Which of the following is a reason due to which the LU decomposition of the system of linear equations;
          x+y = 1, x+y =2 is not possible?
          Select correct option:
          Associated coefficient matrix is singular
          All values of l’s and u’s can’t be evaluated
          Determinant of coefficient matrix is zero
          All are equivalent

          Question # 7 of 10 (Total Marks: 1)
          Gauss - Jordan Method is similar to …
          Select correct option:
          Gauss–Seidel method
          Iteration’s method
          Relaxation Method
          Gaussian elimination method (Page 95)

          Question # 8 of 10 (Total Marks: 1)
          While using Relaxation method, which of the following is the largest Residual for 1st iteration on the
          system; 2x+3y = 1, 3x +2y = - 4 ?
          Select correct option:
          -4
          3
          2
          1

          Question # 9 of 10 (Total Marks: 1)
          Gauss–Seidel method is also known as method of …
          Select correct option:
          Successive displacement (Page 263)
          Iterations
          False position
          None of the given choices

          Question # 10 of 10 (Total Marks: 1)
          Jacobi’s Method is a/an…
          Select correct option:
          Iterative method (Page 69)
          Direct method

          QUIZ.NO.1(2)

          Question # 1 of 10 (Total Marks: 1)
          The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the
          given 3 x 3 identity matrix. where symbol ^ shows power.
          Select correct option:
          (x-1)^3
          (x+1)^3
          x^3-1
          x^3+1

          Question # 2 of 10 (Total Marks: 1)
          The can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue
          the dominant eigenvalue of A.
          Select correct option:
          TRUE
          FALSE

          Question # 3 of 10 (Total Marks: 1)
          In … method, a system is reduced to an equivalent diagonal form using elementary
          transformations.
          Select correct option:
          Jacobi’s
          Gauss-Seidel
          Relaxation
          Gaussian elimination (Page 262)

          Question # 4 of 10 (Total Marks: 1)
          The linear equation: 2x+0y-2=0 has -------- solution/solutions.
          Select correct option:
          Unique (Page 48)
          no solution
          infinite many
          finite many

          Question # 5 of 10 (Total Marks: 1)
          Under elimination methods, we consider, Gaussian elimination and …methods.
          Select correct option:
          Gauss-Seidel
          Jacobi
          Gauss-Jordan elimination (Page 48)
          None of the given choices

          Question # 6 of 10 (Total Marks: 1)
          Which of the following method is not an iterative method?
          Select correct option:
          Jacobi’s method
          Gauss-Seidel method
          Relaxation methods
          Gauss-Jordan elimination method

          Question # 7 of 10 (Total Marks: 1)
          An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal
          to zero.
          Select correct option:
          TRUE
          FALSE (Page 97)

          Question # 8 of 10 (Total Marks: 1)
          Exact solution of 2/3 is not exists.
          Select correct option:
          TRUE
          FALSE

          Question # 9 of 10 (Total Marks: 1)
          When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the
          method is …
          Select correct option:
          Stable
          Unstable
          Convergent (Page 70)
          Divergent

          Question # 10 of 10 (Total Marks: 1)
          Gauss–Seidel method is similar to …
          Select correct option:
          Iteration’s method
          Regula-Falsi method
          Jacobi’s method
          None of the given choices (Page 263)

          QUIZ.NO.1(3)

          Question # 1 of 10 (Total Marks: 1)
          Sparse matrices arise in computing the numerical solution of …
          Select correct option:
          Ordinary differential equations
          Partial differential equations (Page 69)
          Linear differential equations
          Non-linear differential equations

          Question # 2 of 10 (Total Marks: 1)
          While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the
          system; x-2y =1, x+4y=4 ?
          Select correct option:
          (1, 0.75)
          (0,0)
          (1,0)
          (0,1)

          Question # 3 of 10 (Total Marks: 1)
          While solving a system of linear equations by Gauss Jordon Method, after all the elementary row
          operations if there lefts also zeros on the main diagonal then which of the is true about the system?
          Select correct option:
          System may have unique solutions
          System has no solution
          System may have multiple numbers of finite solutions
          System may have infinite many solutions

          Question # 4 of 10 (Total Marks: 1)
          Numerical methods for finding the solution of the system of equations are classified as direct and
          … methods
          Select correct option:
          Indirect
          Iterative (Page 48)
          Jacobi
          None of the given choices

          Question # 5 of 10 (Total Marks: 1)
          If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st
          iteration will reduce to -------.
          Select correct option:
          zero
          4
          -1
          -1

          Question # 6 of 10 (Total Marks: 1)
          While using Relaxation method, which of the following is the Residuals for 1st iteration on the system;
          2x+3y = 1, 3x +2y =4 ?
          Select correct option:
          (2,3)
          (3,-2)
          (-2,3)
          (1,4)

          0= 1-2x-3y
          0= 4-3x -2y

          Question # 7 of 10 (Total Marks: 1)
          If the order of coefficient matrix corresponding to system of linear equations is 33 then which of the
          following will be the orders of its decomposed matrices; ‘L’ and ‘U’?
          Select correct option:
          Order of ‘L’ = 3          1, Order of ‘U’ = 13
          Order of ‘L’ = 3          2, Order of ‘U’ = 2*3

          Order of ‘L’ = 33, Order of ‘U’ = 33
          Order of ‘L’ = 34, Order of ‘U’ = 43

          Question # 8 of 10 (Total Marks: 1)
          While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering
          is feasible to have good approximate solution?
          Select correct option:
          x+4y = 1, x-2y = 4
          x+2y = 1, x- 4y =4
          x+4y = 4, x–2y = 1
          no need to reordering

          Question # 9 of 10 (Total Marks: 1)
          Full pivoting, in fact, is more …than the partial pivoting.
          Select correct option:
          Easiest
          Complicated (Page 51)
          Question # 10 of 10 (Total Marks: 1)
          For the equation
          11fd5b6d-0b86-453d-83b2-64f970116bbc-image.png the root of the equation lies in the interval…

          ► (1, 3)
          ► (1, 2)
          ► (0, 1)
          ► (1, 2)

          QUIZ.NO.1(4)

          Question # 1 of 10 (Total Marks: 1)
          …lies in the category of iterative method.
          ► Bisection Method
          ► Regula Falsi Method
          ► Secant Method
          ► all of the given choices (Page 8)

          Question # 2 of 10 (Total Marks: 1)
          If n x n matrices A and B are similar, then they have the different eigenvalues (with the same
          multiplicities).
          True
          False

          Question # 3 of 10 (Total Marks: 1)
          The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its
          main diagonal.
          No Click here for detail
          At least one

          Question # 4 of 10 (Total Marks: 1)
          If the root of the given equation lies between a and b, then the first approximation to the root of the equation by bisection method is …
          b751921b-b3f6-45cd-9112-ad988bc16051-image.png

          Question # 5 of 10 (Total Marks: 1)
          To apply Simpson’s 3/8 rule, the number of intervals in the following must be
          ► 10
          ► 11
          ► 12
          ► 13

          Question # 6 of 10 (Total Marks: 1)
          The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite
          matrices A.
          Select correct option:
          Positive Click here for detail
          negative

          Question # 7 of 10 (Total Marks: 1)
          Differences methods find the ________ solution of the system.
          Select correct option:
          numerical
          Analytical

          Question # 8 of 10 (Total Marks: 1)
          To apply Simpson’s 1/3 rule, the number of intervals in the following must be
          ► 2 (Simpson’‘s 1/3 rule must use an even number of elements’)
          ► 3
          ► 5
          ► 7

          Question # 9 of 10 (Total Marks: 1)
          Bisection and false position methods are also known as bracketing method and are always
          Divergent
          Convergent (Page 26)
          .67

          Question # 10 of 10 (Total Marks: 1)
          The Inverse of a matrix can only be found if the matrix is
          Singular
          None Singular: Every square non-singular matrix will have an inverse.
          Scalar
          Diagonal

          QUIZ.NO.1(5)

          Question # 1 of 10 (Total Marks: 1)
          In interpolation is used to represent the δ
          Forward difference Δ
          Central difference (Page 117)
          Backward difference

          Question # 2 of 10 (Total Marks: 1)
          The base of the decimal system is _______
          10
          0
          2
          8
          None of the above.

          Question # 3 of 10 (Total Marks: 1)
          Bisection method is … method
          ► Open Method
          ► Bracketing Method (page 26)

          Question # 4 of 10 (Total Marks: 1)
          A 3 x 3 identity matrix have three and __________eigen values.
          same
          different

          Question # 5 of 10 (Total Marks: 1)
          Eigenvalues of a symmetric matrix are all _______ .
          Real (page 104)
          complex
          zero
          positive

          Question # 6 of 10 (Total Marks: 1)
          The Jacobi iteration converges, if A is strictly diagonally dominant.
          TRUE (Page 69)
          FALSE

          Question # 7 of 10 (Total Marks: 1)
          Below are all the finite difference methods EXCEPT _________.
          jacobi’s method
          newton’s backward difference method
          Stirlling formula
          Forward difference method

          Question # 8 of 10 (Total Marks: 1)
          Two matrices with the same characteristic polynomial need not be similar.
          TRUE
          FALSE

          Question # 9 of 10 (Total Marks: 1) No.69
          The determinant of a diagonal matrix is the product of the diagonal elements.
          True
          False

          Question # 10 of 10 (Total Marks: 1)
          The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
          True
          False

          QUIZ.NO.1(6)

          Question # 1 of 10 (Total Marks: 1)
          The determinant of a _______ matrix is the product of the diagonal elements.
          Diagonal Page No.70
          Upper triangular
          Lower triangular
          Scalar

          Question # 2 of 10 (Total Marks: 1)
          For differences methods we require the set of values.
          True
          False

          Question # 3 of 10 (Total Marks: 1)
          If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.
          True
          False

          Question # 4 of 10 (Total Marks: 1)
          Central difference method seems to be giving a better approximation, however it requires more computations.
          True
          False

          Question # 5 of 10 (Total Marks: 1)
          Iterative algorithms can be more rapid than direct methods.
          True
          False

          Question # 6 of 10 (Total Marks: 1)
          Central Difference method is the finite difference method.
          True
          False

          Question # 1 of 10 (Total Marks: 1)
          Back substitution procedure is used in …
          Select correct option:
          Gaussian Elimination Method
          Jacobi’s method
          Gauss-Seidel method
          None of the given choices

          Question # 7 of 10 (Total Marks: 1)
          The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
          True
          False

          Question # 8 of 10 (Total Marks: 1)
          Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.
          True (Page102)
          False

          Question # 9 of 10 (Total Marks: 1)
          Power method is applicable if the eigen values are ______________.
          realanddistinct (Page102)
          real and equal
          positive and distinct
          negative and distinct

          Question # 10 of 10 (Total Marks: 1)
          Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials.
          Quadratic (Page174)
          Linear
          Cubic
          Quartic

          QUIZ.NO.1(7)

          Question # 1 of 10 (Total Marks: 1)
          .In Simpson’s Rule, we use parabolas to approximating each part of the curve. This proves to be very efficient as compared to Trapezoidal rule.
          True Click here for detail
          False

          Question # 2 of 10 (Total Marks: 1)
          The predictor-corrector method an implicit method. (multi-step methods)
          True (Page 212)
          False

          Question # 3 of 10 (Total Marks: 1)
          Generally, Adams methods are superior if output at many points is needed.
          True
          False

          Question # 4 of 10 (Total Marks: 1)
          The Trapezoidal rule is a numerical method that approximates the value of a.______________.
          Indefinite integral
          Definiteintegral (Page176)
          Improper integral
          Function

          Question # 5 of 10 (Total Marks: 1)
          The need of numerical integration arises for evaluating the definite integral of a function that has no
          explicit ____________ or whose anti derivative is not easy to obtain.
          Antiderivative
          Derivatives.

          Question # 6 of 10 (Total Marks: 1)
          An indefinite integral may _________ in the sense that the limit defining it may not exist.
          diverge
          Converge

          Question # 7 of 10 (Total Marks: 1)
          An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or -∞ or, in some cases, as both endpoints approach limits.
          TRUE Click here for detail
          FALSE
          Question # 8 of 10 (Total Marks: 1)
          Euler’s Method numerically computes the approximate derivative of a function.
          TRUE
          FALSE
          Question # 9 of 10 (Total Marks: 1)
          Euler’s Method numerically computes the approximate ________ of a function.
          Antiderivative
          Derivative
          Error
          Value
          Question # 10 of 10 (Total Marks: 1)
          If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the
          infinite limit with a variable, and then take the limit as this variable goes to _________.
          Chose the correct option :
          Constant
          Finite
          Infinity Click here for detail
          Zero

          QUIZ.NO.1(8)

          Question # 1 of 10 (Total Marks: 1)
          The Jacobi iteration ______, if A is strictly diagonally dominant.
          converges
          Diverges
          Question # 2 of 10 (Total Marks: 1)
          By using determinants, we can easily check that the solution of the given system of linear equation exits
          and it is unique.
          TRUE
          FALSE
          Question # 3 of 10 (Total Marks: 1)
          The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of

          13

          matrix A
          TRUE
          FALSE
          Question # 4 of 10 (Total Marks: 1)
          Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.
          TRUE
          FALSE
          Question # 5 of 10 (Total Marks: 1)
          Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero
          vector v such that _______.
          Av = xv
          Ax=xv
          Av + xv=0
          Av = Ax1
          Av = λv
          Question # 6 of 10 (Total Marks: 1)
          In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
          Slow Click here for detail
          Fast
          Question # 7 of 10 (Total Marks: 1)
          Numerical solution of 2/3 up to four decimal places is ________.
          0.667
          0.6666
          0.6667
          0.666671.
          Question # 8 of 10 (Total Marks: 1)
          Symbol used for forward differences is
          ∆ (Page 12)
          δ
          μ
          Question # 9 of 10 (Total Marks: 1)
          The relationship between central difference operator and the shift operator is given by
          δ =Ε−Ε-1
          δ = Ε+Ε-1
          δ = Ε1/2+Ε1/2
          δ = E1/2 −Ε1/2
          1 1
          E E 2 2 
          
           

          (Page 152)
          Question # 10 of 10 (Total Marks: 1)

          14

          Muller’s method requires --------starting points
          1
          2
          3 (Page 41)

          QUIZ.NO.1(9)

          Question # 1 of 10 (Total Marks: 1)
          By using determinants, we can easily check that the solution of the given system of linear equation
          ______ and it is ______.
          Select correct option:
          exits, unique
          exists, consistent
          trivial, unique
          nontrivial, inconsistent
          Question # 2 of 10 (Total Marks: 1)
          Two matrices with the _______ characteristic polynomial need not be similar.
          Select correct option:
          same
          different
          Question # 3 of 10 (Total Marks: 1)
          In … method, the elements above and below the diagonal are simultaneously made zero.
          Select correct option:
          Jacobi’s
          Gauss-Seidel
          Gauss–Jordon Elimination (Page 59)
          Relaxation
          Question # 4 of 10 (Total Marks: 1)
          Which of the following is equivalent form of the system of equations in matrix form; AX=B ?
          Select correct option:
          XA = B
          X = B(Inverse of A)
          X =(Inverse of A)B
          BX = A
          Question # 5 of 10 (Total Marks: 1)
          If the determinant of a matrix A is not equal to zero then the system of equations will have…
          Select correct option:
          a unique solution
          many solutions
          infinite many solutions

          15

          None of the given choices
          Question # 6 of 10 (Total Marks: 1)
          Sparse matrix is a matrix with …
          Select correct option:
          Some elements are zero
          Many elements are zero (page 69)
          Some elements are one
          Many elements are one

          MTH603 – 2

          ND QUIZ FILE (24-11-2011)

          EDIT BY MUHAMMAD AWAIS AND MUHAMMAD MOAAZ SIDDIQ

          QUIZ.NO.2(1)
          Question # 1 of 10 ( Start time: 11:18:07 PM ) Total Marks: 1
          How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
          operator is of differentiation?
          Select correct option:
          Infinite many
          Finite Multiple
          None
          Question # 2 of 10 ( Start time: 11:19:00 PM ) Total Marks: 1
          Which of the following rearrangement make strictly diagonal dominant, the system of linear
          equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?
          Select correct option:
          5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1
          –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9
          5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2
          No need to rearrange as system is already in diagonal dominant form.
          Question # 3 of 10 ( Start time: 11:22:12 PM ) Total Marks: 1
          Which of the following is the meaning of partial pivoting while employing the row transformations?
          Select correct option:
          Making the largest element as pivot (Page 50)
          Making the smallest element as pivot
          Making any element as pivot
          Making zero elements as pivot

          16

          Question # 4 of 10 ( Start time: 11:53:06 PM ) Total Marks: 1
          Differences methods are iterative methods.
          Select correct option:
          TRUE
          FALSE

          Question # 5 of 10 ( Start time: 11:55:28 PM ) Total Marks: 1
          Eigenvalues of a _________ matrix are all real.
          Select correct option:
          symmetric
          antisymmetric
          rectangular
          triangular
          Question # 6 of 10 ( Start time: 11:32:38 PM ) Total Marks: 1
          If a system of equations has a property that each of the equation possesses one large coefficient and
          the larger coefficients in the equations correspond to different unknowns in different equations,
          then which of the following iterative method id preferred to apply?
          Select correct option:
          Gauss-Seidel method
          Gauss-Jordon method
          Gauss elimination method
          Crout’s method
          Question # 7 of 10 ( Start time: 11:35:30 PM ) Total Marks: 1
          For a system of linear equations, the corresponding coefficient matrix has the value of determinant;
          |A| = 0, then which of the following is true?
          Select correct option:
          The system has unique solution
          The system has finite multiple solutions
          The system has infinite may solutions
          The system has no solution (Page 48)
          Question # 8 of 10 ( Start time: 11:36:21 PM ) Total Marks: 1
          For the system; 2x+3y = 1, 3x +2y = - 4, if the iterative solution is (0,0) and ‘dxi = 2’ is the increment
          in ‘y’ then which of the following will be taken as next iterative solution?
          Select correct option:
          (2,0)
          (0,3)
          (0,2)
          (1,-4)

          17

          Question # 9 of 10 ( Start time: 11:37:49 PM ) Total Marks: 1
          While using Relaxation method, which of the following is increment ‘dxi’corresponding to the
          largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?
          Select correct option:
          -2
          2
          3
          4
          Question # 10 of 10 ( Start time: 11:40:42 PM)Total Marks: 1
          If system of equations is inconsistent then its means that it has …
          Select correct option:
          No Solutions
          Many solutions
          Infinite Many solutions
          None of the given choices

          QUIZ.NO.2(2)
          Question # 1 of 10 ( Start time: 11:47:15 PM)Total Marks: 1
          Relaxation Method is a/an …
          Select correct option:
          Direct method
          Iterative method
          Question # 2 of 10 ( Start time: 11:33:36 PM ) Total Marks: 1
          How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
          operator is of differentiation?
          Select correct option:
          Finite Multiple
          Infinite many
          Unique
          None

          Question # 3 of 10 ( Start time: 11:36:46 PM ) Total Marks: 1
          The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the
          matrix, remain … to the original vector.
          Select correct option:
          Perpendicular
          Parallel
          Diagonal

          18

          None of the given choices
          Question # 4 of 10 ( Start time: 11:38:16 PM ) Total Marks: 1
          In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be … to
          the sum of the diagonal elements of the original matrix A.
          Select correct option:
          Greater than
          Less than
          Same (Page 106)
          Different
          Question # 5 of 10 (Total Marks: 1)
          In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric
          matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then
          which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?
          Select correct option:
          Pi/3
          Pi/6
          Pi/2
          Pi/4
          Question # 6 of 10 (Total Marks: 1)
          If f (x) contains trigonometric, exponential or logarithmic functions then this equation is known as
          Transcendental Equation (Page 6)
          Algebraic
          Polynomial
          Linear
          Question # 7 of 10 (Total Marks: 1)
          In interpolation is used to represent the d
          Forward difference ?
          Central difference
          Backward difference
          Question # 8 of 10 (Total Marks: 1)
          The Power method can be used only to find the eigen value of A that is largest in absolute value we call
          this eigen value the dominant eigen value of A.
          True
          False
          Question # 9 of 10 (Total Marks: 1)
          Power method is applicable if the eigen vectors corresponding to eigen values are linearly ----.
          Select correct option:
          independent
          dependent

          cyberianC Offline
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          cyberian
          Cyberian's Cyberian's Gold
          wrote on last edited by
          #39

          @zareen said in MTH603 Mid Term Past and Current Solved Paper Discussion:

          Question # 1 of 10 ( Start time: 11:18:07 PM ) Total Marks: 1
          How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
          operator is of differentiation?
          Select correct option:
          Infinite many
          Finite Multiple
          None

          The correct answer is:

          Infinite many

          The function Exp(ax) = e^ax is an eigenfunction of the differentiation operator, and it has an infinite number of eigenvalues, which are all of the form λ = a. Therefore, there are infinite many eigenvectors corresponding to this function.

          Discussion is right way to get Solution of the every assignment, Quiz and GDB.
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          • zareenZ zareen

            Question # 1 of 10 (Total Marks: 1)
            While solving a system of linear equations, which of the following approach is economical for the computer memory?
            Select correct option:
            Direct
            Iterative (Page 69)
            Analytical
            Graphical

            Question # 2 of 10 (Total Marks: 1)
            The basic idea of relaxation method is to reduce the largest residual to …
            Select correct option:
            One
            Two
            Zero (Page 83)
            None of the given choices

            Question # 3 of 10 (Total Marks: 1)
            The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its
            ________.
            Select correct option:
            main diagonal (Page 104)
            last column
            last row
            first row

            Question # 4 of 10 (Total Marks: 1)
            If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix ,
            the eigenvalues of A are the diagonal entries of A.
            Select correct option:
            TRUE Click here for detail
            FALSE

            Question # 5 of 10 (Total Marks: 1)
            A 3 x 3 identity matrix have three and different eigen values.
            Select correct option:
            TRUE Click here for detail
            FALSE

            Question # 6 of 10 (Total Marks: 1)
            Which of the following is a reason due to which the LU decomposition of the system of linear equations;
            x+y = 1, x+y =2 is not possible?
            Select correct option:
            Associated coefficient matrix is singular
            All values of l’s and u’s can’t be evaluated
            Determinant of coefficient matrix is zero
            All are equivalent

            Question # 7 of 10 (Total Marks: 1)
            Gauss - Jordan Method is similar to …
            Select correct option:
            Gauss–Seidel method
            Iteration’s method
            Relaxation Method
            Gaussian elimination method (Page 95)

            Question # 8 of 10 (Total Marks: 1)
            While using Relaxation method, which of the following is the largest Residual for 1st iteration on the
            system; 2x+3y = 1, 3x +2y = - 4 ?
            Select correct option:
            -4
            3
            2
            1

            Question # 9 of 10 (Total Marks: 1)
            Gauss–Seidel method is also known as method of …
            Select correct option:
            Successive displacement (Page 263)
            Iterations
            False position
            None of the given choices

            Question # 10 of 10 (Total Marks: 1)
            Jacobi’s Method is a/an…
            Select correct option:
            Iterative method (Page 69)
            Direct method

            QUIZ.NO.1(2)

            Question # 1 of 10 (Total Marks: 1)
            The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the
            given 3 x 3 identity matrix. where symbol ^ shows power.
            Select correct option:
            (x-1)^3
            (x+1)^3
            x^3-1
            x^3+1

            Question # 2 of 10 (Total Marks: 1)
            The can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue
            the dominant eigenvalue of A.
            Select correct option:
            TRUE
            FALSE

            Question # 3 of 10 (Total Marks: 1)
            In … method, a system is reduced to an equivalent diagonal form using elementary
            transformations.
            Select correct option:
            Jacobi’s
            Gauss-Seidel
            Relaxation
            Gaussian elimination (Page 262)

            Question # 4 of 10 (Total Marks: 1)
            The linear equation: 2x+0y-2=0 has -------- solution/solutions.
            Select correct option:
            Unique (Page 48)
            no solution
            infinite many
            finite many

            Question # 5 of 10 (Total Marks: 1)
            Under elimination methods, we consider, Gaussian elimination and …methods.
            Select correct option:
            Gauss-Seidel
            Jacobi
            Gauss-Jordan elimination (Page 48)
            None of the given choices

            Question # 6 of 10 (Total Marks: 1)
            Which of the following method is not an iterative method?
            Select correct option:
            Jacobi’s method
            Gauss-Seidel method
            Relaxation methods
            Gauss-Jordan elimination method

            Question # 7 of 10 (Total Marks: 1)
            An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal
            to zero.
            Select correct option:
            TRUE
            FALSE (Page 97)

            Question # 8 of 10 (Total Marks: 1)
            Exact solution of 2/3 is not exists.
            Select correct option:
            TRUE
            FALSE

            Question # 9 of 10 (Total Marks: 1)
            When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the
            method is …
            Select correct option:
            Stable
            Unstable
            Convergent (Page 70)
            Divergent

            Question # 10 of 10 (Total Marks: 1)
            Gauss–Seidel method is similar to …
            Select correct option:
            Iteration’s method
            Regula-Falsi method
            Jacobi’s method
            None of the given choices (Page 263)

            QUIZ.NO.1(3)

            Question # 1 of 10 (Total Marks: 1)
            Sparse matrices arise in computing the numerical solution of …
            Select correct option:
            Ordinary differential equations
            Partial differential equations (Page 69)
            Linear differential equations
            Non-linear differential equations

            Question # 2 of 10 (Total Marks: 1)
            While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the
            system; x-2y =1, x+4y=4 ?
            Select correct option:
            (1, 0.75)
            (0,0)
            (1,0)
            (0,1)

            Question # 3 of 10 (Total Marks: 1)
            While solving a system of linear equations by Gauss Jordon Method, after all the elementary row
            operations if there lefts also zeros on the main diagonal then which of the is true about the system?
            Select correct option:
            System may have unique solutions
            System has no solution
            System may have multiple numbers of finite solutions
            System may have infinite many solutions

            Question # 4 of 10 (Total Marks: 1)
            Numerical methods for finding the solution of the system of equations are classified as direct and
            … methods
            Select correct option:
            Indirect
            Iterative (Page 48)
            Jacobi
            None of the given choices

            Question # 5 of 10 (Total Marks: 1)
            If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st
            iteration will reduce to -------.
            Select correct option:
            zero
            4
            -1
            -1

            Question # 6 of 10 (Total Marks: 1)
            While using Relaxation method, which of the following is the Residuals for 1st iteration on the system;
            2x+3y = 1, 3x +2y =4 ?
            Select correct option:
            (2,3)
            (3,-2)
            (-2,3)
            (1,4)

            0= 1-2x-3y
            0= 4-3x -2y

            Question # 7 of 10 (Total Marks: 1)
            If the order of coefficient matrix corresponding to system of linear equations is 33 then which of the
            following will be the orders of its decomposed matrices; ‘L’ and ‘U’?
            Select correct option:
            Order of ‘L’ = 3            1, Order of ‘U’ = 13
            Order of ‘L’ = 3            2, Order of ‘U’ = 2*3

            Order of ‘L’ = 33, Order of ‘U’ = 33
            Order of ‘L’ = 34, Order of ‘U’ = 43

            Question # 8 of 10 (Total Marks: 1)
            While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering
            is feasible to have good approximate solution?
            Select correct option:
            x+4y = 1, x-2y = 4
            x+2y = 1, x- 4y =4
            x+4y = 4, x–2y = 1
            no need to reordering

            Question # 9 of 10 (Total Marks: 1)
            Full pivoting, in fact, is more …than the partial pivoting.
            Select correct option:
            Easiest
            Complicated (Page 51)
            Question # 10 of 10 (Total Marks: 1)
            For the equation
            11fd5b6d-0b86-453d-83b2-64f970116bbc-image.png the root of the equation lies in the interval…

            ► (1, 3)
            ► (1, 2)
            ► (0, 1)
            ► (1, 2)

            QUIZ.NO.1(4)

            Question # 1 of 10 (Total Marks: 1)
            …lies in the category of iterative method.
            ► Bisection Method
            ► Regula Falsi Method
            ► Secant Method
            ► all of the given choices (Page 8)

            Question # 2 of 10 (Total Marks: 1)
            If n x n matrices A and B are similar, then they have the different eigenvalues (with the same
            multiplicities).
            True
            False

            Question # 3 of 10 (Total Marks: 1)
            The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its
            main diagonal.
            No Click here for detail
            At least one

            Question # 4 of 10 (Total Marks: 1)
            If the root of the given equation lies between a and b, then the first approximation to the root of the equation by bisection method is …
            b751921b-b3f6-45cd-9112-ad988bc16051-image.png

            Question # 5 of 10 (Total Marks: 1)
            To apply Simpson’s 3/8 rule, the number of intervals in the following must be
            ► 10
            ► 11
            ► 12
            ► 13

            Question # 6 of 10 (Total Marks: 1)
            The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite
            matrices A.
            Select correct option:
            Positive Click here for detail
            negative

            Question # 7 of 10 (Total Marks: 1)
            Differences methods find the ________ solution of the system.
            Select correct option:
            numerical
            Analytical

            Question # 8 of 10 (Total Marks: 1)
            To apply Simpson’s 1/3 rule, the number of intervals in the following must be
            ► 2 (Simpson’‘s 1/3 rule must use an even number of elements’)
            ► 3
            ► 5
            ► 7

            Question # 9 of 10 (Total Marks: 1)
            Bisection and false position methods are also known as bracketing method and are always
            Divergent
            Convergent (Page 26)
            .67

            Question # 10 of 10 (Total Marks: 1)
            The Inverse of a matrix can only be found if the matrix is
            Singular
            None Singular: Every square non-singular matrix will have an inverse.
            Scalar
            Diagonal

            QUIZ.NO.1(5)

            Question # 1 of 10 (Total Marks: 1)
            In interpolation is used to represent the δ
            Forward difference Δ
            Central difference (Page 117)
            Backward difference

            Question # 2 of 10 (Total Marks: 1)
            The base of the decimal system is _______
            10
            0
            2
            8
            None of the above.

            Question # 3 of 10 (Total Marks: 1)
            Bisection method is … method
            ► Open Method
            ► Bracketing Method (page 26)

            Question # 4 of 10 (Total Marks: 1)
            A 3 x 3 identity matrix have three and __________eigen values.
            same
            different

            Question # 5 of 10 (Total Marks: 1)
            Eigenvalues of a symmetric matrix are all _______ .
            Real (page 104)
            complex
            zero
            positive

            Question # 6 of 10 (Total Marks: 1)
            The Jacobi iteration converges, if A is strictly diagonally dominant.
            TRUE (Page 69)
            FALSE

            Question # 7 of 10 (Total Marks: 1)
            Below are all the finite difference methods EXCEPT _________.
            jacobi’s method
            newton’s backward difference method
            Stirlling formula
            Forward difference method

            Question # 8 of 10 (Total Marks: 1)
            Two matrices with the same characteristic polynomial need not be similar.
            TRUE
            FALSE

            Question # 9 of 10 (Total Marks: 1) No.69
            The determinant of a diagonal matrix is the product of the diagonal elements.
            True
            False

            Question # 10 of 10 (Total Marks: 1)
            The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
            True
            False

            QUIZ.NO.1(6)

            Question # 1 of 10 (Total Marks: 1)
            The determinant of a _______ matrix is the product of the diagonal elements.
            Diagonal Page No.70
            Upper triangular
            Lower triangular
            Scalar

            Question # 2 of 10 (Total Marks: 1)
            For differences methods we require the set of values.
            True
            False

            Question # 3 of 10 (Total Marks: 1)
            If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.
            True
            False

            Question # 4 of 10 (Total Marks: 1)
            Central difference method seems to be giving a better approximation, however it requires more computations.
            True
            False

            Question # 5 of 10 (Total Marks: 1)
            Iterative algorithms can be more rapid than direct methods.
            True
            False

            Question # 6 of 10 (Total Marks: 1)
            Central Difference method is the finite difference method.
            True
            False

            Question # 1 of 10 (Total Marks: 1)
            Back substitution procedure is used in …
            Select correct option:
            Gaussian Elimination Method
            Jacobi’s method
            Gauss-Seidel method
            None of the given choices

            Question # 7 of 10 (Total Marks: 1)
            The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
            True
            False

            Question # 8 of 10 (Total Marks: 1)
            Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.
            True (Page102)
            False

            Question # 9 of 10 (Total Marks: 1)
            Power method is applicable if the eigen values are ______________.
            realanddistinct (Page102)
            real and equal
            positive and distinct
            negative and distinct

            Question # 10 of 10 (Total Marks: 1)
            Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials.
            Quadratic (Page174)
            Linear
            Cubic
            Quartic

            QUIZ.NO.1(7)

            Question # 1 of 10 (Total Marks: 1)
            .In Simpson’s Rule, we use parabolas to approximating each part of the curve. This proves to be very efficient as compared to Trapezoidal rule.
            True Click here for detail
            False

            Question # 2 of 10 (Total Marks: 1)
            The predictor-corrector method an implicit method. (multi-step methods)
            True (Page 212)
            False

            Question # 3 of 10 (Total Marks: 1)
            Generally, Adams methods are superior if output at many points is needed.
            True
            False

            Question # 4 of 10 (Total Marks: 1)
            The Trapezoidal rule is a numerical method that approximates the value of a.______________.
            Indefinite integral
            Definiteintegral (Page176)
            Improper integral
            Function

            Question # 5 of 10 (Total Marks: 1)
            The need of numerical integration arises for evaluating the definite integral of a function that has no
            explicit ____________ or whose anti derivative is not easy to obtain.
            Antiderivative
            Derivatives.

            Question # 6 of 10 (Total Marks: 1)
            An indefinite integral may _________ in the sense that the limit defining it may not exist.
            diverge
            Converge

            Question # 7 of 10 (Total Marks: 1)
            An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or -∞ or, in some cases, as both endpoints approach limits.
            TRUE Click here for detail
            FALSE
            Question # 8 of 10 (Total Marks: 1)
            Euler’s Method numerically computes the approximate derivative of a function.
            TRUE
            FALSE
            Question # 9 of 10 (Total Marks: 1)
            Euler’s Method numerically computes the approximate ________ of a function.
            Antiderivative
            Derivative
            Error
            Value
            Question # 10 of 10 (Total Marks: 1)
            If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the
            infinite limit with a variable, and then take the limit as this variable goes to _________.
            Chose the correct option :
            Constant
            Finite
            Infinity Click here for detail
            Zero

            QUIZ.NO.1(8)

            Question # 1 of 10 (Total Marks: 1)
            The Jacobi iteration ______, if A is strictly diagonally dominant.
            converges
            Diverges
            Question # 2 of 10 (Total Marks: 1)
            By using determinants, we can easily check that the solution of the given system of linear equation exits
            and it is unique.
            TRUE
            FALSE
            Question # 3 of 10 (Total Marks: 1)
            The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of

            13

            matrix A
            TRUE
            FALSE
            Question # 4 of 10 (Total Marks: 1)
            Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.
            TRUE
            FALSE
            Question # 5 of 10 (Total Marks: 1)
            Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero
            vector v such that _______.
            Av = xv
            Ax=xv
            Av + xv=0
            Av = Ax1
            Av = λv
            Question # 6 of 10 (Total Marks: 1)
            In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
            Slow Click here for detail
            Fast
            Question # 7 of 10 (Total Marks: 1)
            Numerical solution of 2/3 up to four decimal places is ________.
            0.667
            0.6666
            0.6667
            0.666671.
            Question # 8 of 10 (Total Marks: 1)
            Symbol used for forward differences is
            ∆ (Page 12)
            δ
            μ
            Question # 9 of 10 (Total Marks: 1)
            The relationship between central difference operator and the shift operator is given by
            δ =Ε−Ε-1
            δ = Ε+Ε-1
            δ = Ε1/2+Ε1/2
            δ = E1/2 −Ε1/2
            1 1
            E E 2 2 
            
             

            (Page 152)
            Question # 10 of 10 (Total Marks: 1)

            14

            Muller’s method requires --------starting points
            1
            2
            3 (Page 41)

            QUIZ.NO.1(9)

            Question # 1 of 10 (Total Marks: 1)
            By using determinants, we can easily check that the solution of the given system of linear equation
            ______ and it is ______.
            Select correct option:
            exits, unique
            exists, consistent
            trivial, unique
            nontrivial, inconsistent
            Question # 2 of 10 (Total Marks: 1)
            Two matrices with the _______ characteristic polynomial need not be similar.
            Select correct option:
            same
            different
            Question # 3 of 10 (Total Marks: 1)
            In … method, the elements above and below the diagonal are simultaneously made zero.
            Select correct option:
            Jacobi’s
            Gauss-Seidel
            Gauss–Jordon Elimination (Page 59)
            Relaxation
            Question # 4 of 10 (Total Marks: 1)
            Which of the following is equivalent form of the system of equations in matrix form; AX=B ?
            Select correct option:
            XA = B
            X = B(Inverse of A)
            X =(Inverse of A)B
            BX = A
            Question # 5 of 10 (Total Marks: 1)
            If the determinant of a matrix A is not equal to zero then the system of equations will have…
            Select correct option:
            a unique solution
            many solutions
            infinite many solutions

            15

            None of the given choices
            Question # 6 of 10 (Total Marks: 1)
            Sparse matrix is a matrix with …
            Select correct option:
            Some elements are zero
            Many elements are zero (page 69)
            Some elements are one
            Many elements are one

            MTH603 – 2

            ND QUIZ FILE (24-11-2011)

            EDIT BY MUHAMMAD AWAIS AND MUHAMMAD MOAAZ SIDDIQ

            QUIZ.NO.2(1)
            Question # 1 of 10 ( Start time: 11:18:07 PM ) Total Marks: 1
            How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
            operator is of differentiation?
            Select correct option:
            Infinite many
            Finite Multiple
            None
            Question # 2 of 10 ( Start time: 11:19:00 PM ) Total Marks: 1
            Which of the following rearrangement make strictly diagonal dominant, the system of linear
            equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?
            Select correct option:
            5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1
            –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9
            5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2
            No need to rearrange as system is already in diagonal dominant form.
            Question # 3 of 10 ( Start time: 11:22:12 PM ) Total Marks: 1
            Which of the following is the meaning of partial pivoting while employing the row transformations?
            Select correct option:
            Making the largest element as pivot (Page 50)
            Making the smallest element as pivot
            Making any element as pivot
            Making zero elements as pivot

            16

            Question # 4 of 10 ( Start time: 11:53:06 PM ) Total Marks: 1
            Differences methods are iterative methods.
            Select correct option:
            TRUE
            FALSE

            Question # 5 of 10 ( Start time: 11:55:28 PM ) Total Marks: 1
            Eigenvalues of a _________ matrix are all real.
            Select correct option:
            symmetric
            antisymmetric
            rectangular
            triangular
            Question # 6 of 10 ( Start time: 11:32:38 PM ) Total Marks: 1
            If a system of equations has a property that each of the equation possesses one large coefficient and
            the larger coefficients in the equations correspond to different unknowns in different equations,
            then which of the following iterative method id preferred to apply?
            Select correct option:
            Gauss-Seidel method
            Gauss-Jordon method
            Gauss elimination method
            Crout’s method
            Question # 7 of 10 ( Start time: 11:35:30 PM ) Total Marks: 1
            For a system of linear equations, the corresponding coefficient matrix has the value of determinant;
            |A| = 0, then which of the following is true?
            Select correct option:
            The system has unique solution
            The system has finite multiple solutions
            The system has infinite may solutions
            The system has no solution (Page 48)
            Question # 8 of 10 ( Start time: 11:36:21 PM ) Total Marks: 1
            For the system; 2x+3y = 1, 3x +2y = - 4, if the iterative solution is (0,0) and ‘dxi = 2’ is the increment
            in ‘y’ then which of the following will be taken as next iterative solution?
            Select correct option:
            (2,0)
            (0,3)
            (0,2)
            (1,-4)

            17

            Question # 9 of 10 ( Start time: 11:37:49 PM ) Total Marks: 1
            While using Relaxation method, which of the following is increment ‘dxi’corresponding to the
            largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?
            Select correct option:
            -2
            2
            3
            4
            Question # 10 of 10 ( Start time: 11:40:42 PM)Total Marks: 1
            If system of equations is inconsistent then its means that it has …
            Select correct option:
            No Solutions
            Many solutions
            Infinite Many solutions
            None of the given choices

            QUIZ.NO.2(2)
            Question # 1 of 10 ( Start time: 11:47:15 PM)Total Marks: 1
            Relaxation Method is a/an …
            Select correct option:
            Direct method
            Iterative method
            Question # 2 of 10 ( Start time: 11:33:36 PM ) Total Marks: 1
            How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
            operator is of differentiation?
            Select correct option:
            Finite Multiple
            Infinite many
            Unique
            None

            Question # 3 of 10 ( Start time: 11:36:46 PM ) Total Marks: 1
            The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the
            matrix, remain … to the original vector.
            Select correct option:
            Perpendicular
            Parallel
            Diagonal

            18

            None of the given choices
            Question # 4 of 10 ( Start time: 11:38:16 PM ) Total Marks: 1
            In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be … to
            the sum of the diagonal elements of the original matrix A.
            Select correct option:
            Greater than
            Less than
            Same (Page 106)
            Different
            Question # 5 of 10 (Total Marks: 1)
            In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric
            matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then
            which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?
            Select correct option:
            Pi/3
            Pi/6
            Pi/2
            Pi/4
            Question # 6 of 10 (Total Marks: 1)
            If f (x) contains trigonometric, exponential or logarithmic functions then this equation is known as
            Transcendental Equation (Page 6)
            Algebraic
            Polynomial
            Linear
            Question # 7 of 10 (Total Marks: 1)
            In interpolation is used to represent the d
            Forward difference ?
            Central difference
            Backward difference
            Question # 8 of 10 (Total Marks: 1)
            The Power method can be used only to find the eigen value of A that is largest in absolute value we call
            this eigen value the dominant eigen value of A.
            True
            False
            Question # 9 of 10 (Total Marks: 1)
            Power method is applicable if the eigen vectors corresponding to eigen values are linearly ----.
            Select correct option:
            independent
            dependent

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            wrote on last edited by cyberian
            #40

            How to Build a $1,000/Month Portfolio on Upwork in Pakistan (2026 Guide)

            @zareen said in MTH603 Mid Term Past and Current Solved Paper Discussion:

            Which of the following rearrangement make strictly diagonal dominant, the system of linear
            equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?
            Select correct option:
            5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1
            –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9
            5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2
            No need to rearrange as system is already in diagonal dominant form.

            The correct answer is:

            –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9

            To make the system of linear equations strictly diagonal dominant, we need to rearrange the equations such that the absolute value of the diagonal element in each row is greater than the sum of the absolute values of the non-diagonal elements in that row.

            In the given system, the diagonal elements are 1, 4, and -2, respectively. By rearranging the equations as –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9, we get a strictly diagonal dominant system.

            Note that the original system is not already in diagonal dominant form, so option 4 is incorrect.
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            • zareenZ zareen

              Question # 1 of 10 (Total Marks: 1)
              While solving a system of linear equations, which of the following approach is economical for the computer memory?
              Select correct option:
              Direct
              Iterative (Page 69)
              Analytical
              Graphical

              Question # 2 of 10 (Total Marks: 1)
              The basic idea of relaxation method is to reduce the largest residual to …
              Select correct option:
              One
              Two
              Zero (Page 83)
              None of the given choices

              Question # 3 of 10 (Total Marks: 1)
              The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its
              ________.
              Select correct option:
              main diagonal (Page 104)
              last column
              last row
              first row

              Question # 4 of 10 (Total Marks: 1)
              If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix ,
              the eigenvalues of A are the diagonal entries of A.
              Select correct option:
              TRUE Click here for detail
              FALSE

              Question # 5 of 10 (Total Marks: 1)
              A 3 x 3 identity matrix have three and different eigen values.
              Select correct option:
              TRUE Click here for detail
              FALSE

              Question # 6 of 10 (Total Marks: 1)
              Which of the following is a reason due to which the LU decomposition of the system of linear equations;
              x+y = 1, x+y =2 is not possible?
              Select correct option:
              Associated coefficient matrix is singular
              All values of l’s and u’s can’t be evaluated
              Determinant of coefficient matrix is zero
              All are equivalent

              Question # 7 of 10 (Total Marks: 1)
              Gauss - Jordan Method is similar to …
              Select correct option:
              Gauss–Seidel method
              Iteration’s method
              Relaxation Method
              Gaussian elimination method (Page 95)

              Question # 8 of 10 (Total Marks: 1)
              While using Relaxation method, which of the following is the largest Residual for 1st iteration on the
              system; 2x+3y = 1, 3x +2y = - 4 ?
              Select correct option:
              -4
              3
              2
              1

              Question # 9 of 10 (Total Marks: 1)
              Gauss–Seidel method is also known as method of …
              Select correct option:
              Successive displacement (Page 263)
              Iterations
              False position
              None of the given choices

              Question # 10 of 10 (Total Marks: 1)
              Jacobi’s Method is a/an…
              Select correct option:
              Iterative method (Page 69)
              Direct method

              QUIZ.NO.1(2)

              Question # 1 of 10 (Total Marks: 1)
              The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the
              given 3 x 3 identity matrix. where symbol ^ shows power.
              Select correct option:
              (x-1)^3
              (x+1)^3
              x^3-1
              x^3+1

              Question # 2 of 10 (Total Marks: 1)
              The can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue
              the dominant eigenvalue of A.
              Select correct option:
              TRUE
              FALSE

              Question # 3 of 10 (Total Marks: 1)
              In … method, a system is reduced to an equivalent diagonal form using elementary
              transformations.
              Select correct option:
              Jacobi’s
              Gauss-Seidel
              Relaxation
              Gaussian elimination (Page 262)

              Question # 4 of 10 (Total Marks: 1)
              The linear equation: 2x+0y-2=0 has -------- solution/solutions.
              Select correct option:
              Unique (Page 48)
              no solution
              infinite many
              finite many

              Question # 5 of 10 (Total Marks: 1)
              Under elimination methods, we consider, Gaussian elimination and …methods.
              Select correct option:
              Gauss-Seidel
              Jacobi
              Gauss-Jordan elimination (Page 48)
              None of the given choices

              Question # 6 of 10 (Total Marks: 1)
              Which of the following method is not an iterative method?
              Select correct option:
              Jacobi’s method
              Gauss-Seidel method
              Relaxation methods
              Gauss-Jordan elimination method

              Question # 7 of 10 (Total Marks: 1)
              An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal
              to zero.
              Select correct option:
              TRUE
              FALSE (Page 97)

              Question # 8 of 10 (Total Marks: 1)
              Exact solution of 2/3 is not exists.
              Select correct option:
              TRUE
              FALSE

              Question # 9 of 10 (Total Marks: 1)
              When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the
              method is …
              Select correct option:
              Stable
              Unstable
              Convergent (Page 70)
              Divergent

              Question # 10 of 10 (Total Marks: 1)
              Gauss–Seidel method is similar to …
              Select correct option:
              Iteration’s method
              Regula-Falsi method
              Jacobi’s method
              None of the given choices (Page 263)

              QUIZ.NO.1(3)

              Question # 1 of 10 (Total Marks: 1)
              Sparse matrices arise in computing the numerical solution of …
              Select correct option:
              Ordinary differential equations
              Partial differential equations (Page 69)
              Linear differential equations
              Non-linear differential equations

              Question # 2 of 10 (Total Marks: 1)
              While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the
              system; x-2y =1, x+4y=4 ?
              Select correct option:
              (1, 0.75)
              (0,0)
              (1,0)
              (0,1)

              Question # 3 of 10 (Total Marks: 1)
              While solving a system of linear equations by Gauss Jordon Method, after all the elementary row
              operations if there lefts also zeros on the main diagonal then which of the is true about the system?
              Select correct option:
              System may have unique solutions
              System has no solution
              System may have multiple numbers of finite solutions
              System may have infinite many solutions

              Question # 4 of 10 (Total Marks: 1)
              Numerical methods for finding the solution of the system of equations are classified as direct and
              … methods
              Select correct option:
              Indirect
              Iterative (Page 48)
              Jacobi
              None of the given choices

              Question # 5 of 10 (Total Marks: 1)
              If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st
              iteration will reduce to -------.
              Select correct option:
              zero
              4
              -1
              -1

              Question # 6 of 10 (Total Marks: 1)
              While using Relaxation method, which of the following is the Residuals for 1st iteration on the system;
              2x+3y = 1, 3x +2y =4 ?
              Select correct option:
              (2,3)
              (3,-2)
              (-2,3)
              (1,4)

              0= 1-2x-3y
              0= 4-3x -2y

              Question # 7 of 10 (Total Marks: 1)
              If the order of coefficient matrix corresponding to system of linear equations is 33 then which of the
              following will be the orders of its decomposed matrices; ‘L’ and ‘U’?
              Select correct option:
              Order of ‘L’ = 3              1, Order of ‘U’ = 13
              Order of ‘L’ = 3              2, Order of ‘U’ = 2*3

              Order of ‘L’ = 33, Order of ‘U’ = 33
              Order of ‘L’ = 34, Order of ‘U’ = 43

              Question # 8 of 10 (Total Marks: 1)
              While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering
              is feasible to have good approximate solution?
              Select correct option:
              x+4y = 1, x-2y = 4
              x+2y = 1, x- 4y =4
              x+4y = 4, x–2y = 1
              no need to reordering

              Question # 9 of 10 (Total Marks: 1)
              Full pivoting, in fact, is more …than the partial pivoting.
              Select correct option:
              Easiest
              Complicated (Page 51)
              Question # 10 of 10 (Total Marks: 1)
              For the equation
              11fd5b6d-0b86-453d-83b2-64f970116bbc-image.png the root of the equation lies in the interval…

              ► (1, 3)
              ► (1, 2)
              ► (0, 1)
              ► (1, 2)

              QUIZ.NO.1(4)

              Question # 1 of 10 (Total Marks: 1)
              …lies in the category of iterative method.
              ► Bisection Method
              ► Regula Falsi Method
              ► Secant Method
              ► all of the given choices (Page 8)

              Question # 2 of 10 (Total Marks: 1)
              If n x n matrices A and B are similar, then they have the different eigenvalues (with the same
              multiplicities).
              True
              False

              Question # 3 of 10 (Total Marks: 1)
              The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its
              main diagonal.
              No Click here for detail
              At least one

              Question # 4 of 10 (Total Marks: 1)
              If the root of the given equation lies between a and b, then the first approximation to the root of the equation by bisection method is …
              b751921b-b3f6-45cd-9112-ad988bc16051-image.png

              Question # 5 of 10 (Total Marks: 1)
              To apply Simpson’s 3/8 rule, the number of intervals in the following must be
              ► 10
              ► 11
              ► 12
              ► 13

              Question # 6 of 10 (Total Marks: 1)
              The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite
              matrices A.
              Select correct option:
              Positive Click here for detail
              negative

              Question # 7 of 10 (Total Marks: 1)
              Differences methods find the ________ solution of the system.
              Select correct option:
              numerical
              Analytical

              Question # 8 of 10 (Total Marks: 1)
              To apply Simpson’s 1/3 rule, the number of intervals in the following must be
              ► 2 (Simpson’‘s 1/3 rule must use an even number of elements’)
              ► 3
              ► 5
              ► 7

              Question # 9 of 10 (Total Marks: 1)
              Bisection and false position methods are also known as bracketing method and are always
              Divergent
              Convergent (Page 26)
              .67

              Question # 10 of 10 (Total Marks: 1)
              The Inverse of a matrix can only be found if the matrix is
              Singular
              None Singular: Every square non-singular matrix will have an inverse.
              Scalar
              Diagonal

              QUIZ.NO.1(5)

              Question # 1 of 10 (Total Marks: 1)
              In interpolation is used to represent the δ
              Forward difference Δ
              Central difference (Page 117)
              Backward difference

              Question # 2 of 10 (Total Marks: 1)
              The base of the decimal system is _______
              10
              0
              2
              8
              None of the above.

              Question # 3 of 10 (Total Marks: 1)
              Bisection method is … method
              ► Open Method
              ► Bracketing Method (page 26)

              Question # 4 of 10 (Total Marks: 1)
              A 3 x 3 identity matrix have three and __________eigen values.
              same
              different

              Question # 5 of 10 (Total Marks: 1)
              Eigenvalues of a symmetric matrix are all _______ .
              Real (page 104)
              complex
              zero
              positive

              Question # 6 of 10 (Total Marks: 1)
              The Jacobi iteration converges, if A is strictly diagonally dominant.
              TRUE (Page 69)
              FALSE

              Question # 7 of 10 (Total Marks: 1)
              Below are all the finite difference methods EXCEPT _________.
              jacobi’s method
              newton’s backward difference method
              Stirlling formula
              Forward difference method

              Question # 8 of 10 (Total Marks: 1)
              Two matrices with the same characteristic polynomial need not be similar.
              TRUE
              FALSE

              Question # 9 of 10 (Total Marks: 1) No.69
              The determinant of a diagonal matrix is the product of the diagonal elements.
              True
              False

              Question # 10 of 10 (Total Marks: 1)
              The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
              True
              False

              QUIZ.NO.1(6)

              Question # 1 of 10 (Total Marks: 1)
              The determinant of a _______ matrix is the product of the diagonal elements.
              Diagonal Page No.70
              Upper triangular
              Lower triangular
              Scalar

              Question # 2 of 10 (Total Marks: 1)
              For differences methods we require the set of values.
              True
              False

              Question # 3 of 10 (Total Marks: 1)
              If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.
              True
              False

              Question # 4 of 10 (Total Marks: 1)
              Central difference method seems to be giving a better approximation, however it requires more computations.
              True
              False

              Question # 5 of 10 (Total Marks: 1)
              Iterative algorithms can be more rapid than direct methods.
              True
              False

              Question # 6 of 10 (Total Marks: 1)
              Central Difference method is the finite difference method.
              True
              False

              Question # 1 of 10 (Total Marks: 1)
              Back substitution procedure is used in …
              Select correct option:
              Gaussian Elimination Method
              Jacobi’s method
              Gauss-Seidel method
              None of the given choices

              Question # 7 of 10 (Total Marks: 1)
              The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
              True
              False

              Question # 8 of 10 (Total Marks: 1)
              Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.
              True (Page102)
              False

              Question # 9 of 10 (Total Marks: 1)
              Power method is applicable if the eigen values are ______________.
              realanddistinct (Page102)
              real and equal
              positive and distinct
              negative and distinct

              Question # 10 of 10 (Total Marks: 1)
              Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials.
              Quadratic (Page174)
              Linear
              Cubic
              Quartic

              QUIZ.NO.1(7)

              Question # 1 of 10 (Total Marks: 1)
              .In Simpson’s Rule, we use parabolas to approximating each part of the curve. This proves to be very efficient as compared to Trapezoidal rule.
              True Click here for detail
              False

              Question # 2 of 10 (Total Marks: 1)
              The predictor-corrector method an implicit method. (multi-step methods)
              True (Page 212)
              False

              Question # 3 of 10 (Total Marks: 1)
              Generally, Adams methods are superior if output at many points is needed.
              True
              False

              Question # 4 of 10 (Total Marks: 1)
              The Trapezoidal rule is a numerical method that approximates the value of a.______________.
              Indefinite integral
              Definiteintegral (Page176)
              Improper integral
              Function

              Question # 5 of 10 (Total Marks: 1)
              The need of numerical integration arises for evaluating the definite integral of a function that has no
              explicit ____________ or whose anti derivative is not easy to obtain.
              Antiderivative
              Derivatives.

              Question # 6 of 10 (Total Marks: 1)
              An indefinite integral may _________ in the sense that the limit defining it may not exist.
              diverge
              Converge

              Question # 7 of 10 (Total Marks: 1)
              An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or -∞ or, in some cases, as both endpoints approach limits.
              TRUE Click here for detail
              FALSE
              Question # 8 of 10 (Total Marks: 1)
              Euler’s Method numerically computes the approximate derivative of a function.
              TRUE
              FALSE
              Question # 9 of 10 (Total Marks: 1)
              Euler’s Method numerically computes the approximate ________ of a function.
              Antiderivative
              Derivative
              Error
              Value
              Question # 10 of 10 (Total Marks: 1)
              If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the
              infinite limit with a variable, and then take the limit as this variable goes to _________.
              Chose the correct option :
              Constant
              Finite
              Infinity Click here for detail
              Zero

              QUIZ.NO.1(8)

              Question # 1 of 10 (Total Marks: 1)
              The Jacobi iteration ______, if A is strictly diagonally dominant.
              converges
              Diverges
              Question # 2 of 10 (Total Marks: 1)
              By using determinants, we can easily check that the solution of the given system of linear equation exits
              and it is unique.
              TRUE
              FALSE
              Question # 3 of 10 (Total Marks: 1)
              The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of

              13

              matrix A
              TRUE
              FALSE
              Question # 4 of 10 (Total Marks: 1)
              Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.
              TRUE
              FALSE
              Question # 5 of 10 (Total Marks: 1)
              Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero
              vector v such that _______.
              Av = xv
              Ax=xv
              Av + xv=0
              Av = Ax1
              Av = λv
              Question # 6 of 10 (Total Marks: 1)
              In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
              Slow Click here for detail
              Fast
              Question # 7 of 10 (Total Marks: 1)
              Numerical solution of 2/3 up to four decimal places is ________.
              0.667
              0.6666
              0.6667
              0.666671.
              Question # 8 of 10 (Total Marks: 1)
              Symbol used for forward differences is
              ∆ (Page 12)
              δ
              μ
              Question # 9 of 10 (Total Marks: 1)
              The relationship between central difference operator and the shift operator is given by
              δ =Ε−Ε-1
              δ = Ε+Ε-1
              δ = Ε1/2+Ε1/2
              δ = E1/2 −Ε1/2
              1 1
              E E 2 2 
              
               

              (Page 152)
              Question # 10 of 10 (Total Marks: 1)

              14

              Muller’s method requires --------starting points
              1
              2
              3 (Page 41)

              QUIZ.NO.1(9)

              Question # 1 of 10 (Total Marks: 1)
              By using determinants, we can easily check that the solution of the given system of linear equation
              ______ and it is ______.
              Select correct option:
              exits, unique
              exists, consistent
              trivial, unique
              nontrivial, inconsistent
              Question # 2 of 10 (Total Marks: 1)
              Two matrices with the _______ characteristic polynomial need not be similar.
              Select correct option:
              same
              different
              Question # 3 of 10 (Total Marks: 1)
              In … method, the elements above and below the diagonal are simultaneously made zero.
              Select correct option:
              Jacobi’s
              Gauss-Seidel
              Gauss–Jordon Elimination (Page 59)
              Relaxation
              Question # 4 of 10 (Total Marks: 1)
              Which of the following is equivalent form of the system of equations in matrix form; AX=B ?
              Select correct option:
              XA = B
              X = B(Inverse of A)
              X =(Inverse of A)B
              BX = A
              Question # 5 of 10 (Total Marks: 1)
              If the determinant of a matrix A is not equal to zero then the system of equations will have…
              Select correct option:
              a unique solution
              many solutions
              infinite many solutions

              15

              None of the given choices
              Question # 6 of 10 (Total Marks: 1)
              Sparse matrix is a matrix with …
              Select correct option:
              Some elements are zero
              Many elements are zero (page 69)
              Some elements are one
              Many elements are one

              MTH603 – 2

              ND QUIZ FILE (24-11-2011)

              EDIT BY MUHAMMAD AWAIS AND MUHAMMAD MOAAZ SIDDIQ

              QUIZ.NO.2(1)
              Question # 1 of 10 ( Start time: 11:18:07 PM ) Total Marks: 1
              How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
              operator is of differentiation?
              Select correct option:
              Infinite many
              Finite Multiple
              None
              Question # 2 of 10 ( Start time: 11:19:00 PM ) Total Marks: 1
              Which of the following rearrangement make strictly diagonal dominant, the system of linear
              equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?
              Select correct option:
              5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1
              –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9
              5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2
              No need to rearrange as system is already in diagonal dominant form.
              Question # 3 of 10 ( Start time: 11:22:12 PM ) Total Marks: 1
              Which of the following is the meaning of partial pivoting while employing the row transformations?
              Select correct option:
              Making the largest element as pivot (Page 50)
              Making the smallest element as pivot
              Making any element as pivot
              Making zero elements as pivot

              16

              Question # 4 of 10 ( Start time: 11:53:06 PM ) Total Marks: 1
              Differences methods are iterative methods.
              Select correct option:
              TRUE
              FALSE

              Question # 5 of 10 ( Start time: 11:55:28 PM ) Total Marks: 1
              Eigenvalues of a _________ matrix are all real.
              Select correct option:
              symmetric
              antisymmetric
              rectangular
              triangular
              Question # 6 of 10 ( Start time: 11:32:38 PM ) Total Marks: 1
              If a system of equations has a property that each of the equation possesses one large coefficient and
              the larger coefficients in the equations correspond to different unknowns in different equations,
              then which of the following iterative method id preferred to apply?
              Select correct option:
              Gauss-Seidel method
              Gauss-Jordon method
              Gauss elimination method
              Crout’s method
              Question # 7 of 10 ( Start time: 11:35:30 PM ) Total Marks: 1
              For a system of linear equations, the corresponding coefficient matrix has the value of determinant;
              |A| = 0, then which of the following is true?
              Select correct option:
              The system has unique solution
              The system has finite multiple solutions
              The system has infinite may solutions
              The system has no solution (Page 48)
              Question # 8 of 10 ( Start time: 11:36:21 PM ) Total Marks: 1
              For the system; 2x+3y = 1, 3x +2y = - 4, if the iterative solution is (0,0) and ‘dxi = 2’ is the increment
              in ‘y’ then which of the following will be taken as next iterative solution?
              Select correct option:
              (2,0)
              (0,3)
              (0,2)
              (1,-4)

              17

              Question # 9 of 10 ( Start time: 11:37:49 PM ) Total Marks: 1
              While using Relaxation method, which of the following is increment ‘dxi’corresponding to the
              largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?
              Select correct option:
              -2
              2
              3
              4
              Question # 10 of 10 ( Start time: 11:40:42 PM)Total Marks: 1
              If system of equations is inconsistent then its means that it has …
              Select correct option:
              No Solutions
              Many solutions
              Infinite Many solutions
              None of the given choices

              QUIZ.NO.2(2)
              Question # 1 of 10 ( Start time: 11:47:15 PM)Total Marks: 1
              Relaxation Method is a/an …
              Select correct option:
              Direct method
              Iterative method
              Question # 2 of 10 ( Start time: 11:33:36 PM ) Total Marks: 1
              How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
              operator is of differentiation?
              Select correct option:
              Finite Multiple
              Infinite many
              Unique
              None

              Question # 3 of 10 ( Start time: 11:36:46 PM ) Total Marks: 1
              The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the
              matrix, remain … to the original vector.
              Select correct option:
              Perpendicular
              Parallel
              Diagonal

              18

              None of the given choices
              Question # 4 of 10 ( Start time: 11:38:16 PM ) Total Marks: 1
              In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be … to
              the sum of the diagonal elements of the original matrix A.
              Select correct option:
              Greater than
              Less than
              Same (Page 106)
              Different
              Question # 5 of 10 (Total Marks: 1)
              In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric
              matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then
              which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?
              Select correct option:
              Pi/3
              Pi/6
              Pi/2
              Pi/4
              Question # 6 of 10 (Total Marks: 1)
              If f (x) contains trigonometric, exponential or logarithmic functions then this equation is known as
              Transcendental Equation (Page 6)
              Algebraic
              Polynomial
              Linear
              Question # 7 of 10 (Total Marks: 1)
              In interpolation is used to represent the d
              Forward difference ?
              Central difference
              Backward difference
              Question # 8 of 10 (Total Marks: 1)
              The Power method can be used only to find the eigen value of A that is largest in absolute value we call
              this eigen value the dominant eigen value of A.
              True
              False
              Question # 9 of 10 (Total Marks: 1)
              Power method is applicable if the eigen vectors corresponding to eigen values are linearly ----.
              Select correct option:
              independent
              dependent

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              wrote on last edited by
              #41

              @zareen said in MTH603 Mid Term Past and Current Solved Paper Discussion:

              Question # 3 of 10 ( Start time: 11:22:12 PM ) Total Marks: 1
              Which of the following is the meaning of partial pivoting while employing the row transformations?
              Select correct option:
              Making the largest element as pivot (Page 50)
              Making the smallest element as pivot
              Making any element as pivot
              Making zero elements as pivot

              The correct answer is:

              Making the largest element as pivot

              Partial pivoting is a technique used in Gaussian elimination to improve the numerical stability of the method. It involves selecting the largest element in the current column as the pivot element, and then performing row transformations to eliminate the other elements in that column. This helps to reduce the effect of round-off errors and ensure that the solution is accurate.

              By making the largest element as pivot, we can minimize the possibility of dividing by a small number, which can lead to large errors in the solution. This is why partial pivoting is an important step in Gaussian elimination.

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              • zaasmiZ Offline
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                zaasmi
                Cyberian's Gold
                wrote on last edited by
                #42

                In … method, a system is reduced to an equivalent diagonal form using elementary transformations.

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                • zaasmiZ zaasmi

                  In … method, a system is reduced to an equivalent diagonal form using elementary transformations.

                  zaasmiZ Offline
                  zaasmiZ Offline
                  zaasmi
                  Cyberian's Gold
                  wrote on last edited by zaasmi
                  #43

                  @zaasmi said in MTH603 Mid Term Past and Current Solved Paper Discussion:

                  In … method, a system is reduced to an equivalent diagonal form using elementary transformations.

                  Jacobi’s
                  Gaussian elimination
                  Gauss-Seidel
                  Relaxation

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                  • zaasmiZ Offline
                    zaasmiZ Offline
                    zaasmi
                    Cyberian's Gold
                    wrote on last edited by
                    #44

                    While solving a system of three linear equations in three variables by Jacobi’s method, the first approximate solution is NECESSARY to be taken as (0,0,0).

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                    • zaasmiZ zaasmi

                      While solving a system of three linear equations in three variables by Jacobi’s method, the first approximate solution is NECESSARY to be taken as (0,0,0).

                      zaasmiZ Offline
                      zaasmiZ Offline
                      zaasmi
                      Cyberian's Gold
                      wrote on last edited by
                      #45

                      @zaasmi said in MTH603 Mid Term Past and Current Solved Paper Discussion:

                      While solving a system of three linear equations in three variables by Jacobi’s method, the first approximate solution is NECESSARY to be taken as (0,0,0).

                      True
                      False

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                      • zaasmiZ Offline
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                        zaasmi
                        Cyberian's Gold
                        wrote on last edited by zaasmi
                        #46

                        Gauss-Seidel method is similar to …

                        Iteration’s method
                        Regula-Falsi method
                        Jacobi’s method
                        None of the given choices

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                        • zaasmiZ zaasmi

                          Gauss-Seidel method is similar to …

                          Iteration’s method
                          Regula-Falsi method
                          Jacobi’s method
                          None of the given choices

                          zaasmiZ Offline
                          zaasmiZ Offline
                          zaasmi
                          Cyberian's Gold
                          wrote on last edited by
                          #47

                          @zaasmi said in MTH603 Mid Term Past and Current Solved Paper Discussion:

                          Gauss-Seidel method is similar to …

                          Iteration’s method
                          Regula-Falsi method
                          Jacobi’s method
                          None of the given choices

                          Jacobi’s method

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                          • zaasmiZ Offline
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                            zaasmi
                            Cyberian's Gold
                            wrote on last edited by
                            #48

                            While using the Gauss - Seidel Method for finding the solution of the system of equation, the following system
                            3x+y+2=11
                            2x + 5y + z = 16 can be rewritten as
                            x+y+57=4

                            Screenshot 2024-09-11 at 11.53.05 AM.png

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                            • zaasmiZ zaasmi

                              While using the Gauss - Seidel Method for finding the solution of the system of equation, the following system
                              3x+y+2=11
                              2x + 5y + z = 16 can be rewritten as
                              x+y+57=4

                              Screenshot 2024-09-11 at 11.53.05 AM.png

                              zaasmiZ Offline
                              zaasmiZ Offline
                              zaasmi
                              Cyberian's Gold
                              wrote on last edited by zaasmi
                              #49

                              @zaasmi said in MTH603 Mid Term Past and Current Solved Paper Discussion:

                              While using the Gauss - Seidel Method for finding the solution of the system of equation, the following system
                              3x+y+2=11
                              2x + 5y + z = 16 can be rewritten as
                              x+y+57=4

                              Screenshot 2024-09-11 at 11.53.05 AM.png

                              Correct Option: b
                              x=1/3(11 -y-z)
                              y =1/5(16-2x-z)
                              2=1/5(47-x-y)

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                              • zaasmiZ Offline
                                zaasmiZ Offline
                                zaasmi
                                Cyberian's Gold
                                wrote on last edited by
                                #50

                                If the product of two matrices is an identity matrices that is AB = 1, then which of the following is true?

                                A is inverse of B
                                A is singular
                                B is singular
                                A is transpose of B

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                                • zaasmiZ zaasmi

                                  If the product of two matrices is an identity matrices that is AB = 1, then which of the following is true?

                                  A is inverse of B
                                  A is singular
                                  B is singular
                                  A is transpose of B

                                  zaasmiZ Offline
                                  zaasmiZ Offline
                                  zaasmi
                                  Cyberian's Gold
                                  wrote on last edited by
                                  #51

                                  @zaasmi said in MTH603 Mid Term Past and Current Solved Paper Discussion:

                                  If the product of two matrices is an identity matrices that is AB = 1, then which of the following is true?

                                  A is inverse of B
                                  A is singular
                                  B is singular
                                  A is transpose of B

                                  No answer in given option
                                  multiplicative inverse and Properties

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