Given the system C. dx dt dx, f. dt = 4x₁ - 1x₂ a. Write the above system in matrix form ie dx dt b. Find eigenpairs. · = x₁ + 2x₂ = Ax. What is A ? Find ¹A. Can you use eigenmethods? No, because there are not enough eigenpairs. Do long way in class, using the associated homogeneous linear differential equation and find its natural fundamental set of solutions associated to time t =0. Then compare it to the formula 4.15 c in the text. d. Give a general solution of the system. e. Give the solution of the IVP with initial value x(0) = 3 Give the solution of the IVP with initial value x(1) =| (3)

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