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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

Advanced Engineering Mathematics
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 :)

(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
Transcribed Image Text:(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
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) (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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