Find a subset of the vectors that forms a basis for the space spanned by the vectors, then express each vector that is not in the basis as a linear combination of the basis vectors. V₁=(1,0,1,1), V₂ = (-7,7-5,-2), V3 = (-4,7,-2,1), v4 = (-10,7,-8,-5) O V₁, V₂ form the basis; V3 = 3v₁ + V2, V4 = -3V₁ + V2 O V₁, V3, V4 form the basis; V₂ = -4v₁ + V3+7V4 O V2, V3, V4 form the basis; V₁ = 7V₂ + 2V3+3V4 O V₁, V2, V4 form the basis; v3 = -3v₁ + V₂+2V4 O V₁, V2, V3 form the basis; v4 = 3V₁ + V₂ + 3V3

Find a subset of the vectors that forms a basis for the space spanned by the vectors, then express each vector that is not in the basis as a linear combination of the basis vectors. V₁=(1,0,1,1), V₂ = (-7,7-5,-2), V3 = (-4,7,-2,1), v4 = (-10,7,-8,-5) O V₁, V₂ form the basis; V3 = 3v₁ + V2, V4 = -3V₁ + V2 O V₁, V3, V4 form the basis; V₂ = -4v₁ + V3+7V4 O V2, V3, V4 form the basis; V₁ = 7V₂ + 2V3+3V4 O V₁, V2, V4 form the basis; v3 = -3v₁ + V₂+2V4 O V₁, V2, V3 form the basis; v4 = 3V₁ + V₂ + 3V3

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 72E: Proof When V is spanned by {v1,v2,...,vk} and one of these vector can be written as a linear...

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