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Consider the matrix, A = -3 0 T 0 0 3 a) Compute the characteristic polynomial and the eigenvalues of A. b) Why is A diagonalizable? c) Explicitly compute an invertible matrix, S, so that S-¹ AS = D is diagonal. Also write down the r D explicitly. -2 -1 -17

Consider the matrix, A = -3 0 T 0 0 3 a) Compute the characteristic polynomial and the eigenvalues of A. b) Why is A diagonalizable? c) Explicitly compute an invertible matrix, S, so that S-¹ AS = D is diagonal. Also write down the r D explicitly. -2 -1 -17

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 32E
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Consider the matrix, -2 -1 -17) A = -3 0 13 π 0 0 3 a) Compute the characteristic polynomial and the eigenvalues of A. b) Why is A diagonalizable? c) Explicitly compute an invertible matrix, S, so that S-¹ AS = D is diagonal. Also write down the matrix D explicitly.
Transcribed Image Text:Consider the matrix, -2 -1 -17) A = -3 0 13 π 0 0 3 a) Compute the characteristic polynomial and the eigenvalues of A. b) Why is A diagonalizable? c) Explicitly compute an invertible matrix, S, so that S-¹ AS = D is diagonal. Also write down the matrix D explicitly.
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