Let T LPR denote the dierentiation operator on polynomials T

Let T L(P(R)) denote the dierentiation operator on polynomials:

T(p) := p\'

Prove or disprove: I, T, T^2 are linearly independent elements of L(P(R)).

they are linear independent elements.

consider polynomial

x^2

T(x^2) = 2x

T^2(x^2)= 2

all three are LI

$Let T L(P(R)) denote the dierentiation operator on polynomials: T(p) := p\' Prove or disprove: I, T, T^2 are linearly independent elements of L(P(R)).Solutionth$

Let T LPR denote the dierentiation operator on polynomials T

Solution

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