3. Let 6 A = 15 CO CO - NOT NO Oo (a) Find all eigenvalues of A. (b) For each eigenvalue of A find a corresponding eigenvector. (c) Determine a matrix P such that P-AP is a diagonal matrix. (d) Find the general solution to the system of differential equations dx1 = -61 - 2x2 + 23 dt dac 2 = 15x1 + 5x2 - 3x3 dt dx3 = -8x1 - 2x2 + 3x3 dt (e) Find the solution to the above system of differential equations satisfying x1 (0) = 2, x2 (0) = -4, and x3 (0) = 1