A. For v1,v2,v3,v4,v5∈V, {v1,v2,v3,v4,v5} is linearly dependent. B. For v1,v2,v3∈V, span{v1,v2,v3}=V. C. If S={v1,v2,v3} is linearly independent then S is a basis for V. D. If v1,v2,v3∈V then S={v1,v1+v2,v1+v2+v3,v3} is a basis for V. E. If v1,v2,v3,v4∈V and if span{v1,v2,v3,v4}=V then {v1,v2,v3,v4} is a basis for V.

A. For v1,v2,v3,v4,v5∈V, {v1,v2,v3,v4,v5} is linearly dependent. B. For v1,v2,v3∈V, span{v1,v2,v3}=V. C. If S={v1,v2,v3} is linearly independent then S is a basis for V. D. If v1,v2,v3∈V then S={v1,v1+v2,v1+v2+v3,v3} is a basis for V. E. If v1,v2,v3,v4∈V and if span{v1,v2,v3,v4}=V then {v1,v2,v3,v4} is a basis for V.

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 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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