Label the following statements as true or false, and give a brief justification If V is a vector space of dimension n, and if S ⊆ V is a subset of V containing n vectors, then S is linearly independent if and only if S spans V .

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
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Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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Label the following statements as true or false, and give a brief justification

If V is a vector space of dimension n, and if S ⊆ V is a subset of V containing n vectors, then S is linearly
independent if and only if S spans V .

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