Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such that V₁ • V₁ = 42, V₂ · V₂ = 131, V3 · V3 = 9, W.V₁ = -126, w · V₂ = -655, w · V3 = 27, then w = V₁ + V₂+ V3.

Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such that V₁ • V₁ = 42, V₂ · V₂ = 131, V3 · V3 = 9, W.V₁ = -126, w · V₂ = -655, w · V3 = 27, then w = V₁ + V₂+ V3.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 21EQ

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Question

Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such that
V₁ • V₁ = 42, V₂ · V₂ = 131, V3 · V3 = 9,
W.V₁ = -126, w · V₂ = -655, w · V3 = 27,
then w =
V₁ +
V₂+
V3.

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