Problem 5. Let A be a 3 x 3 matrix with real entries and a complex eigenvalue a – ib (b + 0) with corresponding eigenvector ū. Then the other eigenvalues are a + ib and a real number c. Let ū be the eigenvector corresponding to c. Set [c 0 07 C = 0 a P = [w, Reī, Imē] -6 a a) Show that AP PC %3D 1 5 0 1 b) Let A =-5 2 0. Find matrices C and P of the above form such that A = PCP-1. 10 5 c) Diagonalize A

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