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1. Consider the following vectors in R¹: 1 -H The set B = {V1, V2, V3} is a basis of some subspace V of R¹. V₂ = 2 -2 |--D V3 = U= 3 3 2 a) Find an orthogonal basis D = {w₁, W2, W3} of the subspace V. b) Compute the vector proi..u the orthogonal projection of u onto V 3 3 3

1. Consider the following vectors in R¹: 1 -H The set B = {V1, V2, V3} is a basis of some subspace V of R¹. V₂ = 2 -2 |--D V3 = U= 3 3 2 a) Find an orthogonal basis D = {w₁, W2, W3} of the subspace V. b) Compute the vector proi..u the orthogonal projection of u onto V 3 3 3

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 44E: Prove that in a given vector space V, the additive inverse of a vector is unique.
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1. Consider the following vectors in R¹: V₁ = 1 2 0 V3 = 2 -2 3 The set B = {V1, V2, V3} is a basis of some subspace V of Rª. a) Find an orthogonal basis D = {w₁, W2, W3} of the subspace V. b) Compute the vector projvu, the orthogonal projection of u onto V. 3 3 3
Transcribed Image Text:1. Consider the following vectors in R¹: V₁ = 1 2 0 V3 = 2 -2 3 The set B = {V1, V2, V3} is a basis of some subspace V of Rª. a) Find an orthogonal basis D = {w₁, W2, W3} of the subspace V. b) Compute the vector projvu, the orthogonal projection of u onto V. 3 3 3
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