If Span {u,v} = R^2 then {2u,u+v} is a basis for R^2.   Is this statement true?

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 11CM
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If Span {u,v} = R^2 then {2u,u+v} is a basis for R^2.

 

Is this statement true?

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