Question: Define T: Pn R by T[p(x)] = the sum of all the coefficients of p(x). (a) Use the dimension theorem to show that dim(ker

Define T: Pn → R by T[p(x)] = the sum of all the coefficients of p(x).
(a) Use the dimension theorem to show that dim(ker T) = n.
(b) Conclude that (x - 1, x2 - 1,..., xn - 1} is a basis of ker T.

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