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cos ( sin 0 - sin Ꮎ :) Cos

cos ( sin 0 - sin Ꮎ :) Cos

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.5: Eigenvalues And Eigenvectors
Problem 16E
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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
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
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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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)
Transcribed Image Text:= (X) Cose +ising xc950-y ({}) 250-y smo = xyóso --> -y = ix when xcó tixsing So eve x= 1 = y = -2 : - (4)
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