What's the solution of d and e 1. Let T : Pn(R) + Pn+1(R) be defined:...

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What's the solution of d and e

1. Let T : Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) bases {1, X, ..., (a) (2 marks) Show that T is a linear tran

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Answer 1

Answer #1

D:P(R) a. operator → PCR) is the derivative operator. 5 Mon DoT : P (R) —— Pm (IR). is defined by, Dot (broj) D(TC Pene)) D[(

x 1 = (DOT) (1) 7 Wed Ž. (DOT) (W) + **). DoT)(0) Again. (Det) ( 37 +62+47 +8 = 32 +100+8 3x + 10[{-(D•T)(*) +({ }&•7)(0) +8.

Since one [since Þ(n) is a polynomial oso is plx+2), (n+1) is not a polynomial, so only possibility remain exists and that is

TOD:P (R) P. (iR) is defined by 1 sur htl nti (To D)(bn)) T(D.(DOM).) (pers) = (2+1) Þ(x+2) Clearly.ToD is a linear map Cons

der » 1 ie b(n+2) d a constant for some 13 Tue ce pload =d, a constant polynomial Clearly P(n)= d d.1 +0.n tont. +0,21%+0.24+

Answer 2

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