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Prove that a set B = {V₁, V2,..., Un} is a basis of a vector space V if and only if every vector in V can be represented uniquely as a linear combination of vectors in 3.

Prove that a set B = {V₁, V2,..., Un} is a basis of a vector space V if and only if every vector in V can be represented uniquely as a linear combination of vectors in 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 43E: Prove that in a given vector space V, the zero vector is unique.
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. Prove that a set 3 = {V₁, V2, ..., Vn} is a basis of a vector space V if and only if every vector in V can be represented uniquely as a linear combination of vectors in 3.
Transcribed Image Text:. Prove that a set 3 = {V₁, V2, ..., Vn} is a basis of a vector space V if and only if every vector in V can be represented uniquely as a linear combination of vectors in 3.
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