Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. 5 5 5 5 Find the eigenvalues. (Enter your answers as a comma-separated list.) s there a sufficient number to guarantee that the matrix is diagonalizable? O Yes O No

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
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Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be
diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.)
Sufficient Condition for Diagonalization
If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable.
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5 5
5 5
Find the eigenvalues. (Enter your answers as a comma-separated list.)
Is there a sufficient number to guarantee that the matrix is diagonalizable?
O Yes
O No
Transcribed Image Text:Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. [] 5 5 5 5 Find the eigenvalues. (Enter your answers as a comma-separated list.) Is there a sufficient number to guarantee that the matrix is diagonalizable? O Yes O No
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