Problems and solutions - MIT Mathematics
To say that this is an equivalence relation means that symmetry and transitivity hold. Since Sis a subspace, v2Simplies v2Sso v 1 ˘v 2 =)v 1 v 2 2S=)v 2 v 1 2S=)v 2 ˘v 1: Similarly, since it is also possible to add and remain in S v 1 ˘v 2; v 2 ˘v 3 =)v 1 v 2; v 2 v 3 2S=)v 1 v 3 2S=)v 1 ˘v 3: So this is an equivalence relation and the ...
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