Prove that a linearly independent system of vectors v1, V2, . .. , Vn in a vector V is a basis if and only if n = dim V.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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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 linearly independent system of vectors v1, V2, . .. , Vn in a vector
V is a basis if and only if n = dim V.
Transcribed Image Text:Prove that a linearly independent system of vectors v1, V2, . .. , Vn in a vector V is a basis if and only if n = dim V.
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