Suppose that the set {u, v} is linearly independent and that w is NOT in Span{u, v}. Using the definition of linear independence, prove that {u, v, w} is linearly independent.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.CR: Review Exercises
Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...
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Suppose that the set {u, v} is linearly independent and that w is NOT in
Span{u, v}. Using the definition of linear independence, prove that {u, v, w
is linearly independent.
Transcribed Image Text:Suppose that the set {u, v} is linearly independent and that w is NOT in Span{u, v}. Using the definition of linear independence, prove that {u, v, w is linearly independent.
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