Please solve part A B and C for the problem in the photo. I was given one answer but not sure what part it answers so please solve a b and c and ensure one of the answers matches the one supplied in the photo. Please show all steps, calculations, theories and other work done to complete the problem so I can learn the process.

E) a) Write the initial value problem in vector form. b) Solve by using eigenvalues/eigenvectors. c) Write the solution in x(t), y(t) form. 43 dx _ 8x - 9y dt x(0) = 2 dy at = x+2y y(0) = 1 x (t) = 2est - 3test y (t) = est- test. PARTIAL