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. 44. dx = 3x - 5y x(0) = 3 dy dt = 5x - 3y y(0) = 1 x(t) = 3 cos(4t) + sin(4t y(t) = cos(4t) + 3 sin(4t). PARTIAL