The conversation between human and AI assistant.
How do I solve the problem: [math] A=\begin{pmatrix} -2 &4 \\   -5& 7 \end{pmatrix}, A^{n}=? [/math]?
No, I don't. Can you help me figure out how to approach this problem?
Sure. One way to do this is to diagonalize the matrix A, which will give you a diagonal matrix D, such that A can be written as A = PDP^-1, where P is a matrix of eigenvectors of A and D is a diagonal matrix consisting of the eigenvalues of A. From there, you can then raise D to the power of n, which will give you D^n, and then use the formula A^n = PD^nP^-1.