1. Suppose V is the vector space of continuous functions ƒ : [-1, 1] → R.(a) Show that (,): V x V → R given bydefines an inner product.(f,g) = ['ª¸ ƒ(x)g(x)(1 – xa²) dx1(b) Let p(x) = 1 and q(x) = x be elements of V.(i) Calculate the value of ||p|| (with respect to the given inner product).(ii) Calculate the value of ||q|| (with respect to the given inner product).(iii) Calculate the angle between p and q (with respect to the given inner product).

Given a vector space of continuous functions defined by .(a) To show that given definition is an…

Answered: 1. Suppose V is the vector space of…

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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Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are linearly dependent in the vector space C[0,1], but linearly independent in C[1,1].
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