Let T: V → V be a linear operator where dim V = n. If U is a T-invariant subspace of V, let T1 : U → U denote the restriction of T to U (so Tj(u) = T(u) for all u in U). Show that c T(x) = cTI(x) ∙ q(x) for some polynomial q(x). [Hint: Theorem 1.]