For the first order linear system of ODEs: y' (t) = Ay(t), where a -(23) ²). A = Determined the parameter a such that the matrix A has (a): two distinct eigenvalues; (b): a repeated eigenvalue; (c): a pair of conjugate complex eigenvalues. (d): What is the equilibrium of the system? For the conjugate complex eigenvalues, sketch the graphs of the two components y₁ (t) and y2 (t) against time t; and the phase plot assuming y₁ (0) = 1 and y2 (0) = -1.

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