Question: Let T: V V be a linear operator where dim V = n. If U is a T-invariant subspace of V, let T1 :

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.]

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