Chapter 5.7, Problem 1E

A panicle moving in a planar force field has a position vector x that satisfies x′ = Ax. The 2 × 2 matrix A has eigenvalues 4 and 2, with corresponding eigenvectors v₁ = $\left[\begin{array}{l}-3\\ 1\end{array}\right]$ and v₂ = $\left[\begin{array}{l}-1\\ 1\end{array}\right]$. Find the position of the particle at time t, assuming that x(0) = $\left[\begin{array}{l}-6\\ 1\end{array}\right]$.