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3 Let A = . Find, 4 1 a) Find the eigenvalues and eigenvectors of A. b) Verify that det(A) is the product of its eigenvalues. c) Is matrix A diagonalizable? If yes, find matrix P and diagonal matrix D such that A = PDP-¹, otherwise explain why not. d) If matrix A is diagonalizable, compute A" and write the final result as a 2 × 2 matrix.

3 Let A = . Find, 4 1 a) Find the eigenvalues and eigenvectors of A. b) Verify that det(A) is the product of its eigenvalues. c) Is matrix A diagonalizable? If yes, find matrix P and diagonal matrix D such that A = PDP-¹, otherwise explain why not. d) If matrix A is diagonalizable, compute A" and write the final result as a 2 × 2 matrix.

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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2 3 Let A = Find, 4 1 a) Find the eigenvalues and eigenvectors of A. b) Verify that det(A) is the product of its eigenvalues. c) Is matrix A diagonalizable? If yes, find matrix P and diagonal matrix D such that A = PDP-¹, otherwise explain why not. d) If matrix A is diagonalizable, compute A" and write the final result as a 2 × 2 matrix.
Transcribed Image Text:2 3 Let A = Find, 4 1 a) Find the eigenvalues and eigenvectors of A. b) Verify that det(A) is the product of its eigenvalues. c) Is matrix A diagonalizable? If yes, find matrix P and diagonal matrix D such that A = PDP-¹, otherwise explain why not. d) If matrix A is diagonalizable, compute A" and write the final result as a 2 × 2 matrix.
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