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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 standard
basis B={e1,ē2, ē3}:
%3D
10 2
0.
0.
A = |0
3 0
e2 = |1
%3D
0.
1
0.
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 = A1
A 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba35cc5f-959d-4f80-acdd-e9cc0bd31dfa%2F7c6d0ac5-e1c8-4f91-89ce-8aa4c71ac65d%2F6c5a92_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1 The linear transformation T : R3 → R³, T(7) = A, is defined by the matrix A relative to the standard
basis B={e1,ē2, ē3}:
%3D
10 2
0.
0.
A = |0
3 0
e2 = |1
%3D
0.
1
0.
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 = A1
A 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
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