Exercise6

Suppose that \(A\) is a \(2\times2\) matrix having eigenvectors

\begin{equation*} \vvec_1=\twovec{2}{1}, \qquad \vvec_2=\twovec{-1}{2} \end{equation*}

and associated eigenvalues \(\lambda_1=2\) and \(\lambda_2=-3\text{.}\) If \(\xvec=\twovec{5}{0}\text{,}\) find the vector \(A^4\xvec\text{.}\)

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