Question: Define T: Pn Pn by T(p) = p(x) + xp'(x) for all p in Pn. Show that ker T = {0} and conclude that

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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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 full answer

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