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  3. '(16) consider the map t : p2(f) ?p2(f) de?ned by

'(16) Consider the map T : P2(F) ?P2(F) de?ned by T(p(x)) = xp'(x). (a) Prove that T...

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Basic Math

'(16) Consider the map T : P2(F) ?P2(F) de?ned by T(p(x)) =xp'(x).

(a) Prove that T is linear.

(b) What is null(T)?

(c) Compute the matrix M(T) with respect to the bases B and B'of P2(F), where

B = {1,1 + x,1 + x + x2}, B' = {2?x,x + x2,x2}.

(d) Use the matrix M(T) to write T(7x2 + 12x?1) as a linearcombination of the polynomials in the basis B'.

Answer & Explanation Solved by verified expert
3.7 Ratings (410 Votes)
Given TP2FP2Fdefined by Tpx xpx1 Let A ax2bxc and B mx2nxlwhere abcmnl RThen TA x2axb 2ax2bxand TB x2mxn 2mx2nxNow TAB    See Answer
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