4. Let A be a 4×4 matrix. Let 1,-1, 2 be the eigenvalues of A. Suppose that the eigenspace corresponding to the eigenvalue -1 is two dimensional. Can we conclude that A is a diagonalizable matrix? Justify your answer.

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Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
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4. Let A be a 4×4 matrix. Let 1, −1, 2 be the eigenvalues of A. Suppose that
the eigenspace corresponding to the eigenvalue -1 is two dimensional.
Can we conclude that A is a diagonalizable matrix? Justify your answer.
Transcribed Image Text:4. Let A be a 4×4 matrix. Let 1, −1, 2 be the eigenvalues of A. Suppose that the eigenspace corresponding to the eigenvalue -1 is two dimensional. Can we conclude that A is a diagonalizable matrix? Justify your answer.
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