Please show your working clearly that's readable as it will help me understand better. Thank you!

Part A

Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. *1 Ii:r b. Find the real-valued solution to the initial value problem Use t as the independent variable in your answers. MU) = l:l 920) = l_l _. '01: Li 3y1 + 2m, 5yl 3% Solve the system 03:13 _ 3 9 3 dt _ _1 _3 2 with 3(0) 2 4 Give your solution in real form. Consider the initial value problem y' = 12 7 3 + 9(t), 3(1) = 0. Suppose we know that tta y (t ) = [3t2 + B] is the unique solution to this initial value problem. Find g(t) and the constants a and B. a= B = g(t) =