Question: Consider the matrices (a) Verify that they are diagonalizable and that they commute. (b) Find the eigenvalues and eigenvectors of A and verify that its

Consider the matrices

A = 2 - 1 2 - 1 2 -1 2 2

(a) Verify that they are diagonalizable and that they commute.
(b) Find the eigenvalues and eigenvectors of A and verify that its spectrum is degenerate.
(c) Are the eigenvectors that you found in part (b) also eigenvectors of B? If not, find the vectors that are simultaneous eigenvectors of both matrices.

A = 2 - 1 2 - 1 2 -1 2 2 B= 2 - 1 2 -1 2 -1 15 -1 2

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a Since Ay A and By B the matrices are normal Equation A82 and hence diagonalizable b To get ... View full answer

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