Question: Problem 4. Let A be a 3 x 3 matrix with real entries and a complex eigenvalue a - ib (b * 0) with corresponding

Problem 4. Let A be a 3 x 3 matrix with real entries and a complex eigenvalue a - ib (b * 0) with corresponding eigenvector v. Then the other eigenvalues are a + ib and a real number c. Let w be the eigenvector corresponding to c. Set O O C = 0 P = [w, Rev, Imu] a a) Show that AP = PC 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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