Question: Define T: P P by setting T(p) =p, where p(t) = p(t)- tp(1) for all real t. You may assume that T is linear.

Define T: P P by setting T(p) =p, where p(t) = p(t)- tp(1) for all real t. You may assume that T is linear. Find a set of polynomials that span the null space of T, and a set of polynomials that span the range of T.

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