10. Let T be a linear operator on a finite-dimensional vector space V, and suppose that W is a T-invariant subspace of V. Prove that the minimal polynomial of Tw divides the minimal polynomial of T. 10. Let p(t) be the minimal polynomial of T. Thus we have p(Tw)(w) = p(T)(w) = 0 for all we W. This means that p(Tw) is a zero mapping. Hence the minimal polynomial of Tw divides p(t).