Chapter 5.3, Problem 4E

In Exercises 3 and 4, use the factorization A = PDP⁻¹ to compute A^k, where k represents an arbitrary positive integer.

4. $\left[\begin{array}{cc}-2& 12\\ -1& 5\end{array}\right]=\left[\begin{array}{cc}3& 4\\ 1& 1\end{array}\right]\left[\begin{array}{cc}2& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cc}-1& 4\\ 1& -3\end{array}\right]$