MTH303 - Mathematical Methods

Assignment#2 MTH303 (Fall 2019) DON’T MISS these important instructions: Total marks: 10 Lecture#29-31 Due date: January 26, 2020  Upload assignments properly through LMS.  All students are directed to use the font and style of text as is used in this document.  This is an individual assignment, not group assignment, so keep in mind that you are supposed to submit your own and self-made assignment even if you discuss the questions with your class fellows. All similar assignments (even with some meaningless modifications) will be awarded zero marks and no excuse will be accepted. This is your responsibility to keep your assignment safe from others.  Solve the assignment on MS word document. Question#1 ⃗ Consider a linear transformation 𝑇: 𝑅2 → 𝑅2 defined by 𝑇(𝑥) = 𝐴(𝑥) then verify that 𝑇(𝑢⃗ +𝑣)=𝑇(𝑢⃗ ) + 𝑡(𝑣), where [image: LsESgmW.png] Question#2 Let 𝑇: 𝑅2 → 𝑅3 be a linear transformation such that defined by 𝑇(𝑥1, 𝑥2) = (𝑥1 − 2𝑥2, −𝑥1 + 3𝑥2, 3𝑥1 − 2𝑥2). Find 𝑥 such that 𝑇(𝑥) = (−1,4,9)

1 Assignment#1 MTH303 (Fall 2019) Total marks: 20 Lecture#7-15 Due date: December 6, 2019 DON’T MISS these important instructions: • Upload assignments properly through LMS. • All students are directed to use the font and style of text as is used in this document. • This is an individual assignment, not group assignment, so keep in mind that you are supposed to submit your own and self-made assignment even if you discuss the questions with your class fellows. All similar assignments (even with some meaningless modifications) will be awarded zero marks and no excuse will be accepted. This is your responsibility to keep your assignment safe from others. • Solve the assignment on MS word document. Question#1 Determine the associated Auxiliary equation of [image: vXC5MBv.png] Question#2 Determine whether the functions are linearly dependent or independent. [image: bIm8qK8.png]