4. Suppose V

. Suppose V is a vector space and that L : V > V is a linear map. For a positive integer 71, dene L" to be the nfold composition of L with itself. That is, L1 (13') = L(17), L207) = L(L(')), L3(') = L(L(L())), and so on. (a) Assume V is nite dimensional. Prove that there is some positive integer n such that ker(L") = ker(Lm) for every m 2 n. (b) Give an example to show that if V is not nite dimensional then the statement in part (a) is not necessarily true