Suppose A = [ A²: 13 -30 5 -12 Find an invertible matrix P and a diagonal matrix D so that A = PDP-1. Use your answer to find an expression for A7 in terms of P, a power of D, and P-¹ in that order. 38188

Suppose a 3x 3 matrix A admits a factorization as A =PDP¯1 where Pis some invertible matrix and D is the diagonal matrix shown to the right. Show that this factorization is useful when computing high 3 0 D= powers of A. Find fairly simple formulas for A?, A°, and A" (k a positive integer), using P and the entries in D.

Find a matrix A such that 6 4 A A ГОТ = 13 5 4 8-4 A