For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal. (If not possible, enter IMPOSSIBLE.) A =      2    0    0           −4    5    −1      −1    0    5 P =      Verify that P−1AP is a diagonal matrix with the eigenvalues on the main diagonal. P−1AP =

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 55E
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For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal. (If not possible, enter IMPOSSIBLE.)
A = 
    2    0    0     
     −4    5    −1
     −1    0    5
P =
    
Verify that P−1AP is a diagonal matrix with the eigenvalues on the main diagonal.
P−1AP =
                

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