Please help me the last two parts. Part E and F. Make sure include part F i and ii, although please type by computer thank you 1 The linear transformation T : R3 → R³, T(7) = A, is defined by the matrix A relative to the standardbasis B={e1,ē2, ē3}:%3D10 20.0.A = |03 0e2 = |1%3D0.10.A. Find the eigenvalues {A;} for A.&Find the set of orthornormal eigenvectors {pi}.E Show that the P = [Pi P2 p3] is symmetric, i.e. PT = P-1%3|9. Show that D = PT AP =0.E Bonus. Show that pi Api = A1A D is the matrix for T with respect to the eigenbasis B'={pi,P2, P3}.i. Is P from 3. the transition matrix from B' to B?Hint: Does [B' B] → [I P¯1] produce the same P?ii. What do each of the eigenvectors look like with respect to the eigenbasis?Hint: [Pi]B = P-1 [Pi]B:%3D

Name: Please help me the last two parts. Part E and F. Make sure include par
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Description: Please help me the last two parts. Part E and F. Make sure include part F i and ii, although please type by computer thank you 1 The linear transformation T : R3 → R³, T(7) = A, is defined by the matrix A relative to the standardbasis B={e1,ē2, ē3}:%

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E Bonus. Show that pi" Api = 1 4 D is the matrix for T with respect to the eigenbasis B'={p1,P2, P3}. i. Is P from 3. the transition matrix from B' to B? Hint: Does [B' B] → [I P-1] produce the same P? ii. What do each of the eigenvectors look like with respect to the eigenbasis? Hint: [P1]B

E Bonus. Show that pi" Api = 1 4 D is the matrix for T with respect to the eigenbasis B'={p1,P2, P3}. i. Is P from 3. the transition matrix from B' to B? Hint: Does [B' B] → [I P-1] produce the same P? ii. What do each of the eigenvectors look like with respect to the eigenbasis? Hint: [P1]B

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.4: Orthogonal Diagonalization Of Symmetric Matrices

Problem 27EQ

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