Define T: Pn R by T[p(x)] = the sum of all the coefficients of p(x). (a)

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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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Linear Algebra With Applications

ISBN: 9780070985100

7th Edition

Authors: W. Keith Nicholson

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Question Posted: Jun 21, 2016 06:44 AM

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Define T: Pn R by T[p(x)] = the sum of all the coefficients of p(x). (a)

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b Write B x 1 x 2 1 x n 1 Then B 20 k er T because Tx k 1 1 1 0 for al...View the full answer

Linear Algebra With Applications

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