Chapter 5.6, Problem 2E

Suppose the eigenvalues of a 3 × 3 matrix A are 3, 4/5, and 3/5, with corresponding eigenvectors $\left[\begin{array}{l}1\\ 0\\ -3\end{array}\right]$, $\left[\begin{array}{l}2\\ 1\\ -5\end{array}\right]$, and $\left[\begin{array}{l}-3\\ -3\\ 7\end{array}\right]$. Let x₀ = $\left[\begin{array}{l}-2\\ -5\\ 3\end{array}\right]$. Find the solution of the equation x_k+1 = Ax_k for the specified x₀, and describe what happens