
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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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 ⃗
Consider a linear transformation 𝑇: 𝑅2 → 𝑅2 defined by 𝑇(𝑥) = 𝐴(𝑥) then verify that
𝑇(𝑢⃗ +𝑣)=𝑇(𝑢⃗ ) + 𝑡(𝑣), where
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#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
Question#2
Determine whether the functions are linearly dependent or independent.
MTH303 Assignment 2 Solution and Discussion

Assignment#2 MTH303 (Fall 2019)
DON’T MISS these important instructions:
Total marks: 10 Lecture#2931 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 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 ⃗
Consider a linear transformation 𝑇: 𝑅2 → 𝑅2 defined by 𝑇(𝑥) = 𝐴(𝑥) then verify that
𝑇(𝑢⃗ +𝑣)=𝑇(𝑢⃗ ) + 𝑡(𝑣), where
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) 
Some Liner transformation Examples:

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