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proof of the following statement If S= {v1, v2, ...., vr} is a nonempty set of...

proof of the following statement

If S= {v1, v2, ...., vr} is a nonempty set of vectors in a vector space V then : W is the smallest subspace of V that contains all of the vectors in S in the sense that any other subspace of V that contains those vectors must contain W.

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