9. Let W be a subspace of an inner product space V. The orthogonal complement of W is the setw- = {v € V : (v, w) = 0 for all w E W}.(a) Prove that W Ow+ = {0}.(b) Prove that W+ is a subspace of V.(c) Prove that if W = span{u1,..., u,} then W- = {v € V such that (v, u;) = 0 for all i = 1, ...,r}.

A subspace is a term from linear algebra. Members of a subspace are all vectors, and they all have…

Let W be a subspace of an inner product space V. The orthogonal complement of W is the set w+ = {v € V : (v, w) = 0 for all w E W}. (a) Prove that Wn Ww+ = {0}. (b) Prove that W+ is a subspace of V. (c) Prove that if W = span{u1,..., u,} then W+ = {v € V such that (v, u;) = 0 for all i = 1, ...,r}.

Let W be a subspace of an inner product space V. The orthogonal complement of W is the set w+ = {v € V : (v, w) = 0 for all w E W}. (a) Prove that Wn Ww+ = {0}. (b) Prove that W+ is a subspace of V. (c) Prove that if W = span{u1,..., u,} then W+ = {v € V such that (v, u;) = 0 for all i = 1, ...,r}.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 4AEXP

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