The system of differential equations is given as 1-a 1-a - [₁ i] a a-1 x': = x, where a is a constant parameter. (a) Find the critical value of a where the qualitative nature of the phase portrait changes. (b) Choose a value of a below the critical value and establish the general solution. What type of equilibrium (the origin point at the phase portrait) corresponds to the chosen a? (c) Choose a value of a above the critical value and establish the general solution. What type of equilibrium (the origin point at the phase portrait) corresponds to the chosen a? (d) For the critical value of a, what are the phase trajectories and how many equilibria are there?

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