(17) Let 0 A = 1 0-2) 2 1 1 0 3 (a) Determine the characteristic polynomial of A, the eigenvalues of A and their algebraic multi- plicities (b) Find bases for the eigenspaces of A. Determine the geometric multiplicities of each eigenvalue. (c) Is A diagonalizable. Justify your reason. (d) If A diagonalizable, write down an invertible matrix P and a diagonal matrix D such that A = PDP-¹. Otherwise explain why A is not diagonalizable.

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