Problem 3.4 (6 points). We will prove, in steps, that ker(L)=ker(LL) for any LRnm (a) Prove that ker(L)ker(LL). (b) Prove that if y is a vector satisfying yTy=0, then y=0. (c) Use part (b) to deduce that if x is a vector satisfying xTLTLx=0, then Lx=0. (d) Use part (c) to deduce that ker(LL)ker(L)