please send step by step handwritten solution Q4 part a 4.Consider the following linear mapT: P3 → P3defined as follows:T(ao + a1x + a2r² + a3x*) = ao + a1(r+ 2) + a2(x+ 2)² + a3(x+3)*(ao + 2a1 + 4a2 + 8a3) + (a1 + 4az + 12a3)r + (a2 + 6a3)r² + azr%3Da) Determine if it is an isomorphism.b) Determine if r + 2x? is in the image of T.

Answered: Image /qna-images/answer/be8bc64f-a9df-4ffc-b7d3-5ac630c0a28a.jpg

Consider the following linear map T: P3 → P3 defined as follows: T(ao + a1r + azx² + azx³) = ao + a(r+ 2) + a2(x+ 2)² + a3(x + 3)³ = (ao + 2a1 + 4az + 8a3) + (a1 + 4a2 + 12a3)r + (a2 + 6a3)x² + a3r³ %3D a) Determine if it is an isomorphism.

Consider the following linear map T: P3 → P3 defined as follows: T(ao + a1r + azx² + azx³) = ao + a(r+ 2) + a2(x+ 2)² + a3(x + 3)³ = (ao + 2a1 + 4az + 8a3) + (a1 + 4a2 + 12a3)r + (a2 + 6a3)x² + a3r³ %3D a) Determine if it is an isomorphism.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 5CM: Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).

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Question

please send step by step handwritten solution Q4 part a

4.
Consider the following linear map
T: P3 → P3
defined as follows:
T(ao + a1x + a2r² + a3x*) = ao + a1(r+ 2) + a2(x+ 2)² + a3(x+3)*
(ao + 2a1 + 4a2 + 8a3) + (a1 + 4az + 12a3)r + (a2 + 6a3)r² + azr
%3D
a) Determine if it is an isomorphism.
b) Determine if r + 2x? is in the image of T.

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