Let V be an inner product space. Prove that:(a) if weV is orthogonal to each of the vectors u,,u,...,u, eV , then w is orthogonalto every vector in (u,,uz,…..,u;).(b) if {v,v,..,v,} is a basis of V, show that the zero vector is the only vector in Vthat is orthogonal to all basis vectors vi, i= 1,2, ... , n.

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Let V be an inner product space. Prove that: (a) if weV is orthogonal to each of the vectors u,„u,,..,u̟ eV , then w is orthogonal to every vector in L(u,,uz,…..,u̟). (b) if {v,v½,...,v̟} is a basis of V, show that the zero vector is the only vector in V that is orthogonal to all basis vectors V;, i= 1, 2, ... , n.

Let V be an inner product space. Prove that: (a) if weV is orthogonal to each of the vectors u,„u,,..,u̟ eV , then w is orthogonal to every vector in L(u,,uz,…..,u̟). (b) if {v,v½,...,v̟} is a basis of V, show that the zero vector is the only vector in V that is orthogonal to all basis vectors V;, i= 1, 2, ... , n.

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 33EQ

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