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]?
Yes, that makes sense. But how do I find the eigenvectors and eigenvalues of A?
To find the eigenvalues of A, you can solve the characteristic equation det(A - λI) = 0, where I is the identity matrix and λ is the eigenvalue. Once you have the eigenvalues, you can then find the eigenvectors associated with each eigenvalue by solving the equation (A - λI)v = 0, where v is the eigenvector.