3. Consider the following matrix M = 0 (a) Find the eigenvalues and eigenvectors of M. (b) Prove by induction that 1k k k-1 k(k-1) k-2 2 M* = 0 kk- 1 0 0 (c) Hence, show that eat text exp(Mt) = 0 eat text 0 0 edt (d) Show that the general solution to y = My is y ( t ) = a (" tele + telin textp ) + B ( tell[ + elin ) + yells (1) for constants a, 3, y and where & is an eigenvector of M and where (M-AI)n = $ and (M-AD)p =