1 0 0 Let A = -3 1 3 3 0-2 (a) Find all eigenvalues of A. (b) For each eigenvalue A of A, find a basis of the eigenspace Nul (AI - A). (c) If possible, diagonalize A; that is, find an invertible matrix PE R3×3 and a diagonal matrix D = R³×³ such that A = PDP-¹. (d) Given a positive integer k, compute and simplify A.

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