Consider the system T1 = T2 = The eigenvectors are dx dt where x is a 2 x 1 vector. a) Find the eigenvalues r₁, 72 and the corresponding eigenvectors. 1 (³² 3-20 -5 X 2)-(5 and P) 1 b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. The origin is a [Choose one and is Choose one c) Sketch, by hand (without using any graphing device), several trajectories in the phase plane. d) Use an appropriate graphing device to plot accurately several trajectories in the phase plane and the corresponding graphs of a versus t and x2 versus t.

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