Please need answer the first 4 parts part a part B part C and pard D. Please type the answer 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, e2, ē3}:%3D10.0 2A = 0 302 0ei =0.10.10.A. Find the eigenvalues {A;} for A.2 Find the set of orthornormal eigenvectors {pi}.E Show that the P = Pi P2 p3] is symmetric, i.e. PT = P-1%3D%3D0.0.9. Show that D = PT AP =%3D0.T.E Bonus. Show that pi' Api = A14 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'| produce the same P?ii. What do each of the eigenvectors look like with respect to the eigenbasis?Hint: Pi]p = P Pi]B:%3D

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Description: Please need answer the first 4 parts part a part B part C and pard D. Please type the answer 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, e2, ē3}:%3D10.0 2A =

Let A be a matrix of order n and lambda be any scalar, then a non-zero vector x is called as eigen…

Answered: 4. Find the eigenvalues {A;} for A. 2…

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4. Find the eigenvalues {A;} for A. 2 Find the set of orthornormal eigenvectors {pi}. E Show that the P= [P1 P2 P3] is symmetric, i.e. PT = P-1 %3D 9. Show that D = PT AP = 0. 0. %3D %3D 0.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 29EQ

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Please need answer the first 4 parts part a part B part C and pard D. Please type the answer 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, e2, ē3}:
%3D
1
0.
0 2
A = 0 30
2 0
ei =
0.
1
0.
1
0.
A. Find the eigenvalues {A;} for A.
2 Find the set of orthornormal eigenvectors {pi}.
E Show that the P = Pi P2 p3] is symmetric, i.e. PT = P-1
%3D
%3D
0.
0.
9. Show that D = PT AP =
%3D
0.
T.
E Bonus. Show that pi' Api = A1
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'| produce the same P?
ii. What do each of the eigenvectors look like with respect to the eigenbasis?
Hint: Pi]p = P Pi]B:
%3D

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