MATH 1004 Lecture 1: math 1004 - SEPT 7 2017

If a R, let Ea : P rightarrow R be evaluation at a, that is Ea [p (x)] = p (a) for every polynomial p (x) Show that Ea (xk) = [E (x)]k for all k 0, where we write [p (x)) degree = 1 for every polynomial p (x). If T : P rightarrow R is any linear transformation such that T (xk) = [T (X)]K for all k 0. show that T - Ea for some real number a.