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January 2, 2021 10:25 pm 30 pts
Mathenmatics-vA (MSP Eduncle ifferentiable Let W = C°(R) be the vector space of all C real-valued functions (smooth function, differentiah 22 for all degree of differentiation). W. Let V be the vector space of all linear transformations from vv The addition and the scalar multiplication of V are given by those of linear transtormations. Let T, T, T be the elements in V defined by d T,(f(x)=fx) dx T(f(x))= f(X) T,(f(x)= f(t)dt Then which of the following is correct? the set {T,,T,,T} are linearly independent (A) the set {T,,T,,T} are linearly dependent T, is Linear combination of T, and T, (B) (C) (D) None of these
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• Satpal singh
take f as constant function. set will contain zero vector. option A and C are wrong by this. take f=x^2+1 by this option B is wrong. so option D is right according to me