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.

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
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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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