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 DiagonalizationIf an n × n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. 11 11Find the eigenvalues. (Enter your answers as a comma-separated list.)? = Is there a sufficient number to guarantee that the matrix is diagonalizable?YesNo 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 shownbelow.)Sufficient Condition for DiagonalizationIf an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable.Find the eigenvalues. (Enter your answers as a comma-separated list.)Is there a sufficient number to guarantee that the matrix is diagonalizable?O YesO No

Answered: Find the eigenvalues of the matrix and…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.4: Orthogonal Diagonalization Of Symmetric Matrices

Problem 27EQ

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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 × n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable.