Define T: Pn Pn by T(p) = p(x) + xp'(x) for all p in Pn. Show

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Define T: Pn → Pn by T(p) = p(x) + xp'(x) for all p in Pn.
Show that ker T = {0} and conclude that T is an isomorphism. [Write p(x) = a0 + a1x + ∙ ∙ ∙ ∙ + anxn and compare coefficients if p(x) = - xp'(x).]

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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 06:45 AM

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Define T: Pn Pn by T(p) = p(x) + xp'(x) for all p in Pn. Show

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If px is in ker T then px xp x If we write px a 0 a 1 x a n x n this becomes a 0 ...View the full answer

Linear Algebra With Applications

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