3.* Let X be the vector space of continuous real valued functions in [-1, 1]. Define (·, ·) : X×X → Ras(x, y)= | x(1) y(1) dt.(a) Show that (', ·) is a inner product.(b) Let Y c X be the set of even continuous real valued functions in [-1, 1]. That is,y € Yy(t) = y(-1) Vt e [-1, 1].Let Zc X be the set of odd continuous real valued functions in [-1, 1]. That is,z E Zz(t) = -z(-1) VtE [-1,1].Show that Y IZ.

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Answered: * Let X be the vector space of…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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