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.3. Let 7 : R² → R² be defined by Ty) = y. Is T a linear transfo ustify your answer. If T is a linear transformation find its matrix relati tandard basis of R². • (³D) = [ + ] ₁ on? Justify your answer. If T is a linear transformation find its matrix .4. Let T R2 R2 be defined by T : Is T a linear tra

.3. Let 7 : R² → R² be defined by Ty) = y. Is T a linear transfo ustify your answer. If T is a linear transformation find its matrix relati tandard basis of R². • (³D) = [ + ] ₁ on? Justify your answer. If T is a linear transformation find its matrix .4. Let T R2 R2 be defined by T : Is T a linear tra

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
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I'm struggling to solve this problem solely using matrix notation, and I need your guidance. The problem specifically requires a solution using matrix notation exclusively, without any other methods. Can you please provide a thorough, step-by-step explanation in matrix notation to help me reach the final solution?

it has to be done the matrix way thank you

Additionally, I have attached the question and answer to both problems. Could you demonstrate the matrix approach leading up to the solution?

2 7.3. Let T: R² → R² be defined by T R² be defined by T (X) = E]. y Justify your answer. If T is a linear transformation find its matrix relative to the standard basis of R². 7.4. Let T: R2 R2 be defined by T ->> Is T a linear transformation? X y+ +1] y Is T a linear transforma- tion? Justify your answer. If T is a linear transformation find its matrix relative to the standard basis of R².
Transcribed Image Text:2 7.3. Let T: R² → R² be defined by T R² be defined by T (X) = E]. y Justify your answer. If T is a linear transformation find its matrix relative to the standard basis of R². 7.4. Let T: R2 R2 be defined by T ->> Is T a linear transformation? X y+ +1] y Is T a linear transforma- tion? Justify your answer. If T is a linear transformation find its matrix relative to the standard basis of R².
7.3 Yes. T T (3)+()=== Hence T (+)-¹(₁+x) - [+] = T Also, T +T y2 X2 X2 (]+[D= (*)+¹(₂) +T T Y₁ + y₂ V₁ + V2] CX cy T (₁ED = ¹ (13) = 1 = ] = ₁ (E) T C cT 7.4 No. T(0) ‡ 0. Matrix of T relative to standard basis is [T]
Transcribed Image Text:7.3 Yes. T T (3)+()=== Hence T (+)-¹(₁+x) - [+] = T Also, T +T y2 X2 X2 (]+[D= (*)+¹(₂) +T T Y₁ + y₂ V₁ + V2] CX cy T (₁ED = ¹ (13) = 1 = ] = ₁ (E) T C cT 7.4 No. T(0) ‡ 0. Matrix of T relative to standard basis is [T]
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