Consider the initial value problem 31 = 692, y1 (0) = -1, y = -By1 + 12y2, 92(0) = 1. a. Find the eigenvalue >, an eigenvector 71, and a generalized eigenvector v2 for the coefficient matrix of this linear system. = 181 0 1 = 6 1 02 = b. Find the most general real-valued solution to the linear system of differential equations. Use ci and C2 to denote arbitrary constants, and enter them as c1 and c2. 31(t) = cleot + c2e6t yz(t) = cleof + 1 c2e61 + 1 cze6t c. Solve the original initial value problem. y1 (t) =-e6t + 12te6t 32 (t) = e6t + 12te6t