Chapter 5.7, Problem 6E

In Exercises 3–6, solve the initial value problem x′(t) = Ax(t) for t ≥ 0, with x(0) = (3, 2). Classify the nature of the origin as an arc actor, repeller, or saddle point of the dynamical system described by x′ = Ax. Find the directions of greatest attraction and/or repulsion. When the origin is a saddle point, sketch typical trajectories.

6. A = $\left[\begin{array}{cc}1& -2\\ 3& -4\end{array}\right]$