3. Let V denote the vector space of all functions ƒ : R → R, equipped with addition + : V × V → V definedvia (ƒ + g)(x) = f(x) + g(x), x € R, and scalar multiplication · : R × V → V defined via (\ · ƒ)(x) = \ƒ(x),xERnNow let W = {ƒ : R → R : ƒ(x) = ax + b for some a, b ≤ R}, i.e. the space of all linear functions R → R.(a) Show that W is a subspace of V. (You may assume that V is a vector space).(b) Find a basis for W. You should prove that it is indeed a basis.

(a) Given that V is a vector space of all real functions defined on real number. W= {It is given…

Answered: 3. Let V denote the vector space of all…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

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