#6: Given a system defined by the following matrix differential equation, complete the tasks listed. The objective of this problem is to solve the system of differential equations, using the eigenvalue approach. It is a powerful tool that you will be required to know. du(t) = Au(t) = 1-2 31 u(t). dt - 2 -3 a) By hand, find the eigenvalues and eigenvectors for matrix A. Associate eigenvalue li with eigen- vector q and similarly for 12. Verify your results with Python. (5 pts) b) Write the diagonal matrix, A, having diagonal elements that are the eigenvalues from part (a). Then write the matrix et (5 pts) c) Write the matrix S = q 22). Note, this implies that X1 is the first element in A. If you did it opposite, be sure to adjust S appropriately. Then determine S-l by hand and write down the answer. (5 pts)