Suppose that A is a diagonalizable matrix that has been written in the form A PDP 1, where D is diagonal (a) Show that for positive integer k, Ak PDkP 1 (b) Use the result of part (a) to compute A50 deg for (c) Show that if D is diagonal, then Dk is diagonal (d) Is the equation in part (a) true for k 1 Could this be useful in finding the inverse of a matrix A 4

Question: Suppose that A is a diagonalizable matrix that has been written in the form A = PDP-1, where D is diagonal. (a) Show that for

Suppose that A is a diagonalizable matrix that has been written in the form A = PDP-1, where D is diagonal.
(a) Show that for positive integer k, Ak = PDkP-1.
(b) Use the result of part (a) to compute A50° for

(c) Show that if D is diagonal, then Dk is diagonal.
(d) Is the equation in part (a) true for k = -1? Could this be useful in finding the inverse of a matrix?

A = [ ] 4

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