dy/dx - = 1 - y,y(0) = 0 is an example of

[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

[zaasmi]

@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

[zaasmi]

While using the relaxation method for finding the solution of the following system
8x1+3x2-2x3=5
4x1+7×2+2x3=9 with the initial vector(0, 0, 0), the residuals would be
3X1+5x2+9x3=2

R1 = 3, R2 = 7, R3 = 6
R1 = 2, R2 = 6, R3 = 3
R1 = 5, R2 = 9, R3 = 2
R1=-4, R2 = 8, R3 = 9

[zaasmi]

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

While using the relaxation method for finding the solution of the following system
8x1+3x2-2x3=5
4x1+7×2+2x3=9 with the initial vector(0, 0, 0), the residuals would be
3X1+5x2+9x3=2

R1 = 3, R2 = 7, R3 = 6
R1 = 2, R2 = 6, R3 = 3
R1 = 5, R2 = 9, R3 = 2
R1=-4, R2 = 8, R3 = 9

R1 = 3, R2 = 7, R3 = 6

[zaasmi]

Gauss-Seidel method is also known as method of …

False position

Iterations

None of the given choices

Successive displacement

[zaasmi]

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

Gauss-Seidel method is also known as method of …

False position

Iterations

None of the given choices

Successive displacement

Successive displacement

[raza rajpoot]

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

Gauss-Seidel method is also known as method of …

Gauss–Seidel method is an improved form of Jacobi method, also known as the successive displacement method. This method is named after Carl Friedrich Gauss (Apr.

[zaasmi]

Sparse matrix is a matrix with …

Select the correct option:
Many elements are one
Some elements are one
Some elements are zero
Many elements are zero

[zaasmi]

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

Sparse matrix is a matrix with …

Select the correct option:
Many elements are one
Some elements are one
Some elements are zero
Many elements are zero

Many elements are zero

[sanwal mazhar]

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

Sparse matrix is a matrix with …

A sparse matrix is a special case of a matrix in which the number of zero elements is much higher than the number of non-zero elements. As a rule of thumb, if 2/3 of the total elements in a matrix are zeros, it can be called a sparse matrix.

[zaasmi]

While using Gaussian Elimination method, the following augmented matrix

[zaasmi]

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

While using Gaussian Elimination method, the following augmented matrix

Correct Answer: A

[zaasmi]

While using the relaxation method for finding the solution of the following system
5x1+12-3x3=5
x1 +5x2 +2x3 = 7 with the initial vector(0, 0, 0), the residuals would be
x1 +2×2+4x3=3

Select the correct option
R1 = 3, R2 = 2, R3 = 1
R1 = 2, R2 = 1, R3 = 1
R1 = 5, R2 = 7, R3 = 3
R1 = 1,R2 = 3, R3 = 2

[zaasmi]

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

While using the relaxation method for finding the solution of the following system
5x1+12-3x3=5
x1 +5x2 +2x3 = 7 with the initial vector(0, 0, 0), the residuals would be
x1 +2×2+4x3=3

Select the correct option
R1 = 3, R2 = 2, R3 = 1
R1 = 2, R2 = 1, R3 = 1
R1 = 5, R2 = 7, R3 = 3
R1 = 1,R2 = 3, R3 = 2

R1 = 5, R2 = 7, R3 = 3

[zaasmi]

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)

[zaasmi]

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

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)

To solve the system of equations using the Gauss-Seidel method, we first need to rearrange each equation to solve for one variable in terms of the other. Given the system:

1. ( x - 2y = 1 )
2. ( x + 4y = 4 )

Rearrange these equations:

1. ( x = 1 + 2y )
2. ( x = 4 - 4y )

At the first iteration, we start with initial guesses. A common starting point is ( (0, 0) ), though other choices might be used depending on the problem.

Using ( (x_0, y_0) = (0, 0) ):

1. For ( x ): ( x = 1 + 2y )
   [ x_1 = 1 + 2 \cdot 0 = 1 ]

2. For ( y ): Use the updated ( x ) value from step 1.
   [ y = \frac{4 - x}{4} ]
   [ y_1 = \frac{4 - 1}{4} = \frac{3}{4} = 0.75 ]

Thus, the first iterative solution with the initial guess ( (0,0) ) is ( (1, 0.75) ).

So the correct option is:

(1, 0.75).