[EX5 Q1 Diagonalisation] could u please answer the circled question step by step on image1? And the solution is on the image2, thx :) (a) eigenvalues: 1, −2; eigenvectors:4 3(1¹)-(3), P = (19)4(b) eigenvalues: cos 0+i sin 0, cos 0-i sin 0; eigenvectors:(c) igenvalues -2, -2, 0, eigenvectors:919-2000~651 P11-1(C)-(C)-P-(7)9-i9-1i1 -121 -2 31 2 1 1. Find the eigenvalues of each of the following matrices A over the complex numbersC. For each eigenvalue find one corresponding eigenvector, and then write downa matrix P such that PAP-¹ is diagonal.(a)(b)(c)109-12 -11COS Asin 0- sin 0-3 -2113)COSAT-T10 12-1

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Find the eigenvalues of each of the following matrices A over the complex numbers C. For each eigenvalue find one corresponding eigenvector, and then write down a matrix P such that PAP-¹ is diagonal. (a) (b) 10 9 (-12-11) cos ( - sin Ꭿ sin 0 cos -3 1 -2 0 2 1 -1

Find the eigenvalues of each of the following matrices A over the complex numbers C. For each eigenvalue find one corresponding eigenvector, and then write down a matrix P such that PAP-¹ is diagonal. (a) (b) 10 9 (-12-11) cos ( - sin Ꭿ sin 0 cos -3 1 -2 0 2 1 -1

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 10AEXP

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Question

[EX5 Q1 Diagonalisation] could u please answer the circled question step by step on image1? And the solution is on the image2, thx :)

(a) eigenvalues: 1, −2; eigenvectors:
4 3
(1¹)-(3), P = (19)
4
(b) eigenvalues: cos 0+i sin 0, cos 0-i sin 0; eigenvectors:
(c) igenvalues -2, -2, 0, eigenvectors:
9
1
9
-2
000~65
1 P
1
1
-1
(C)-(C)-P-(7)
9
-i
9
-1
i
1 -1
2
1 -2 3
1 2 1

1. Find the eigenvalues of each of the following matrices A over the complex numbers
C. For each eigenvalue find one corresponding eigenvector, and then write down
a matrix P such that PAP-¹ is diagonal.
(a)
(b)
(c)
10
9
-12 -11
COS A
sin 0
- sin 0
-3 -2
1
1
3)
COSA
T-T
1
0 1
2
-1

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