1. Consider the following linear systems of ordinary differential equations: (a) dx/dt = 3x – 2y, dy/dt = 2x – 2y (b) dx/dt = x - 5y, dy/dt = x – 3y For each of the system: (i) Find the eigenvalues...

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Extracted text: 1. Consider the following linear systems of ordinary differential equations: (a) dx/dt = 3x – 2y, dy/dt = 2x – 2y (b) dx/dt = x - 5y, dy/dt = x – 3y For each of the system: (i) Find the eigenvalues and eigenvectors of each linear system. (ii) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable.