DO NOT WANT AI SOLUTION. Thank You Consider the inner product space (R³, (,)), where(u,v) = Av, Vu, v € R³,andLetand define the set12 1A=25212 3=-(9)S = {€ R³ |is orthogonal to },which can be shown to be a subspace of R3. Find a basis for S.

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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 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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Consider the inner product space (R³, (,)), where (u,v) = Av, Vu, v € R³, and Let and define the set 1 2 1 A= 2 52 1 2 3 =-(9) S = {€ R³ | is orthogonal to }, which can be shown to be a subspace of R3. Find a basis for S.