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If V is a linear space and S is a proper subset of V, and...

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Advance Math

If V is a linear space and S is a proper subset of V, and wedefine a relation on V via v1 ~ v2 iff v1 - v2 are in S, a subspaceof V. We are given ~ is an equivalence relation, show that the setof equivalence classes, V/S, is a vector space as well, where thetypical element of V/S is v + s, where v is any element of V.

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