Question: Consider the dynamical system x k + 1 = Ax k . (a) Compute and plot x 0 ,x 1 ,x 2 ,x 3 ,

Consider the dynamical system

x_k + 1 = Ax_k.

(a) Compute and plot x₀,x₁,x₂,x₃, for x₀ Consider the dynamical systemxk + 1 = Axk.(a) Compute and

(b) Compute and plot x₀,x₁,x₂,x₃, for x₀(c) Using eigenvalues and eigenvectors, classify the origin as an attractor, repeller, saddle point, or none of these.
(d) Sketch several typical trajectories of the system.

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