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a) For the matrix A below, find the eigenvalues, the eigenvectors, a basis B for which the matrix [LA]s is diagonal and the change of basis matrix from the standard basis of R³ to B. A = 200 -245 0 1 0 -4 2 b) For which values of r does the matrix A = -[7 ] have real eigenvalues? I -2 c) Take z = -1 and find the eigenvectors of A.

a) For the matrix A below, find the eigenvalues, the eigenvectors, a basis B for which the matrix [LA]s is diagonal and the change of basis matrix from the standard basis of R³ to B. A = 200 -245 0 1 0 -4 2 b) For which values of r does the matrix A = -[7 ] have real eigenvalues? I -2 c) Take z = -1 and find the eigenvectors of A.

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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1. a) For the matrix A below, find the eigenvalues, the eigenvectors, a basis B for which the matrix [LA]B is diagonal and the change of basis matrix from the standard basis of R³ to B. 2 00 A = -2 4 5 1 -4 b) For which values of a does the matrix A = -[ ] have real eigenvalues? I c) Take z = -1 and find the eigenvectors of A. 0 0 2 -2
Transcribed Image Text:1. a) For the matrix A below, find the eigenvalues, the eigenvectors, a basis B for which the matrix [LA]B is diagonal and the change of basis matrix from the standard basis of R³ to B. 2 00 A = -2 4 5 1 -4 b) For which values of a does the matrix A = -[ ] have real eigenvalues? I c) Take z = -1 and find the eigenvectors of A. 0 0 2 -2
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