Question: 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,

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.

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