Can you do f through h, but please do all the parts in the question? 2. Find all eigenvalues and a corresponding eigenvector for each matrix below without cal-culations by thinking it out using the linear transformation's geometric interpretation.Write a few words (like 5) in each case explaining why your eigenvector/eigenvalue pairworks. For each matrix, graph each eigenvector and it's image after the transformation aswell as a random NON-eigenvector. Check your graph is accurate by showing the matrixmultiplication.(а) АTA = id.[1(b) АTA =projection onto x-axis.[cos(0) – sin(0)[sin(8) cos(0)(and state the values of 0 for which A has eigenvectors)(с) АTA =rotation by 0.[0 1(d) АTA =reflect about the line "y = x".(е) АTA =stretch in x-direction.0 1(f) ATA =shear.[1 0 0]0 1 0, TA =stretch z-axis.(g) A0 0 2][1 00 0 -1|,TA=rotate by 90° about the x-axis.0 1(h) A=

We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Answered: (f) A= 0 1

Math

Advanced Math

(f) A= 0 1

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.5: Iterative Methods For Computing Eigenvalues

Problem 15EQ

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Question

Can you do f through h, but please do all the parts in the question?

2. Find all eigenvalues and a corresponding eigenvector for each matrix below without cal-
culations by thinking it out using the linear transformation's geometric interpretation.
Write a few words (like 5) in each case explaining why your eigenvector/eigenvalue pair
works. For each matrix, graph each eigenvector and it's image after the transformation as
well as a random NON-eigenvector. Check your graph is accurate by showing the matrix
multiplication.
(а) А
TA = id.
[1
(b) А
TA =projection onto x-axis.
[cos(0) – sin(0)
[sin(8) cos(0)
(and state the values of 0 for which A has eigenvectors)
(с) А
TA =rotation by 0.
[0 1
(d) А
TA =reflect about the line "y = x".
(е) А
TA =stretch in x-direction.
0 1
(f) A
TA =shear.
[1 0 0]
0 1 0, TA =stretch z-axis.
(g) A
0 0 2]
[1 0
0 0 -1|,TA=rotate by 90° about the x-axis.
0 1
(h) A=

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