Consider the initial value problem i = Ar with a(0) = 2o € R where 1. = T0 %3D -1 0 0 A = 0 10 0 1 1 and to X2 X3, (a) Find three linearly independent solutions of the ODE system i = Ar. (b) For what values of X1, X2 and X3 is the solution to the initial value problem bounded on R,? = xo which are bounded in (c) Find the set of all solutions to i = Ar with a(0) R+.

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A: We use definition of nilopotent matrix.

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A: Since you have asked multiple part question, we will solve the first 3 part of thequestion for you…

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