[EX5 Q1 Diagonalisation] could u please answer the circled question step by step on image1? And the solution is on the image2, thx :) -34 3(1). (3). P = (1³).4(a) eigenvalues: 1, -2; eigenvectors:(b) eigenvalues: cos 0+isin 0, cos 0-i sin 0; eigenvectors:(c) eigenvalues -2, -2,0, eigenvectors:--1(1). (C)² = ( 7 ).P229ii222(0) 0011991)1P =1 - 1 21-2 312 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 down.a matrix P such that PAP-¹ is diagonal.(a)el10-12COSsin 09-11- sin 0COS

Answered: Image /qna-images/answer/86550349-8585-4882-be7a-a7e6c5d06587.jpg

Answered: cos ( sin 0 - sin Ꮎ :) Cos

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

-3
4 3
(1). (3). P = (1³).
4
(a) eigenvalues: 1, -2; eigenvectors:
(b) eigenvalues: cos 0+isin 0, cos 0-i sin 0; eigenvectors:
(c) eigenvalues -2, -2,0, eigenvectors:
-
-1
(1). (C)² = ( 7 ).
P
2
2
9
i
i
2
2
2
(0) 00
1
1
9
9
1)
1
P =
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)
el
10
-12
COS
sin 0
9
-11
- sin 0
COS

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I try to use the eigenvalue to find eigenvector, and I've already found the relation between x and y. I can substitute x=1 and get y=-i, but the solution provided is substituting x=-1 and get y=i. There is a problem, how can I know which value of x should I choose?