In Exercises 3-6, solve the initial value problem x'(t) = Ax(t) for t > 0, with x(0)

Question:

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 attractor, 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.
1.