4.W.2 Let A be the matrix below, and consider the dynamical system Ik+1 = Ark. This is basically the same as the previou

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4 W 2 Let A Be The Matrix Below And Consider The Dynamical System Ik 1 Ark This Is Basically The Same As The Previou 1 (99.23 KiB) Viewed 29 times

4.W.2 Let A be the matrix below, and consider the dynamical system Ik+1 = Ark. This is basically the same as the previous problem, but I don't make you compute specific points on trajectories. You should still compute some points (using computer algebra software) when sketching trajec- tories carefully .6 A= -.5 0 = [ -> ] 11 a) Find the eigenvalues and eigenspaces of A, and graph these lines on the plane. b) Carefully sketch the trajectories through [1] and [ 0.5 1.5 ] c) Loosely sketch other trajectories of this dynamical system, including at least one trajectory with each kind of behavior. Include all special trajectories (i.e. trajectories of eigenvectors). Trajectories should have arrows indicating direction (as k increases).