Let A be a 3 x 3 diagonalizable matrix whose eigenvalues are A1 =-3, A2 = -2, and A3 = 1. If V1 = [1 0 0], V2 = [1 1 0], V3 = [0 1 1] are eigenvectors of A corresponding to A1, d2, and Ag, respectively, then factor A into a product XDX-1with D diagonal, and use this factorization to find A5.

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