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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.
4. A =
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Linear Algebra and Its Applications (5th Edition)
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