cos ( sin 0 - sin Ꮎ :) Cos
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 30EQ
Related questions
Question
[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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc76f7391-61d3-4396-8738-502514b3b1a1%2F86550349-8585-4882-be7a-a7e6c5d06587%2Fykoutpj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:-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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc76f7391-61d3-4396-8738-502514b3b1a1%2F86550349-8585-4882-be7a-a7e6c5d06587%2Fsqoft4u_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
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?
![= (X)
Cose +ising
xc950-y
({})
250-y smo = xyóso
-->
-y = ix
when
xcó tixsing
So eve
x= 1 = y = -2
:
- (4)](https://content.bartleby.com/qna-images/question/c76f7391-61d3-4396-8738-502514b3b1a1/7fed208d-9f54-48f5-8653-061127c8d748/3bsaoj7_thumbnail.jpeg)
Transcribed Image Text:= (X)
Cose +ising
xc950-y
({})
250-y smo = xyóso
-->
-y = ix
when
xcó tixsing
So eve
x= 1 = y = -2
:
- (4)
Solution
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