Chapter 5.7, Problem 2E

Let A be a 2 × 2 matrix with eigenvalues −3 and −1 and corresponding eigenvectors v₁ = $\left[\begin{array}{l}-1\\ 1\end{array}\right]$ and v₂ = $\left[\begin{array}{l}1\\ 1\end{array}\right]$. Let x(t) be the position of a panicle at time t. Solve the initial value problem x′ = Ax, x(0) = $\left[\begin{array}{l}2\\ 3\end{array}\right]$.