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

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

Expert Solution

Colby Messinger answered 2 years ago

Proof: Let S ⊆ V be a subset of a vector space V over F. We...

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Let S be a subset of a vector space V . Show that span(S) = span(span(S))....

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Let U be a subset of a vector space V. Show that spanU is the intersection...

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(1) Suppose that V is a vector space and that S = {u,v} is a set...

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