Let u be some fixed vector in R" and let S be the set of all vectors in R" that are orthogonal to u. IsSa subspace of R"? Be sure to justify your answer by showing explicitly how it either passes all thepart of the subspace test or how it fails one of them.

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Answered: Let ū be some fixed vector in R" and…

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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Let ū be some fixed vector in R" and let S be the set of all vectors in R" that are orthogonal to ū. Is Sa subspace of R"? Be sure to justify your answer by showing explicitly how it either passes all the part of the subspace test or how it fails one of them.