Lecture 20: Linear Algebra (span of a subset S is the smallest subspace containing S)

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Span of a subset S is the smallest subspace containing S. #Mathsforall #Gate #NET #UGCNET @Mathsforall
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why is span(S) the smallest subspace? I understand that it's because the Theorem says it is, but why does the theorem when state that it must be the smallest?

javieraranazelaya