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In this question, as usual, e1, e2, e3 are the standard basis vectors for R 3...

In this question, as usual, e1, e2, e3 are the standard basis vectors for R 3 (that is, ej has a 1 in the jth position, and has 0 everywhere else). (a) Suppose that D is a 3 × 3 diagonal matrix. Show that e1, e2, e3 are eigenvectors of D. (b) Suppose that A is a 3 × 3 matrix, and that e1, e2, and e3 are eigenvectors of A. Is it true that A must be a diagonal matrix? If so, explain why. If not, give a specific example of a non-diagonal matrix A for which e1, e2, and e3 are eigenvectors.

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