Some Liner transformation Examples:

Assignment#2 MTH303 (Fall 2019)
DON’T MISS these important instructions:
Total marks: 10 Lecture#2931 Due date: January 26, 2020
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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
30e92d97c9914d059277cc2fbd8e30f0image.pngQuestion#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#715
Due date: December 6, 2019DON’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 selfmade 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 2d287df0a0bf4860a0c28dc9e0b3b8c7image.png
Question#2
Determine whether the functions are linearly dependent or independent.
f8b18ae0234140198f2574c7340a6de0image.png