Let 1 2 -1 0 -1 3 0 1 0 A = -5 6 4 3 -3 8 -8 -6-5 2 3 -4 -3 -3 2 (a) (3 points) Verify that 0-0 and are eigenvectors of A. a (b) (2 points) Find a vector v = C for some a, b, c, d E R such that Avv. Show your workings d 1 clearly. (c) (2 points) Using the vector v defined in part (b), find a generalized eigenvector associated to 1. Show your workings clearly. (d) (7 points) Hence, solve the initial value problem y = Y1 = +2y2 -91 + 3y2 Y5 Ys + 34 - -5y1 +672 +4y3 + 3y4 - 3ys = 81 812 5y + 245 - 3y1 - 4y2 3y4 +2y5 with initial condition 1(0) 1, 2(0)=1, 3(0)=1, 34(0)1, ys(0) = 1. Note, you must use all the information from part(a) to part(c) above. Show your workings clearly.