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Span(S1 ∩ S2) ⊆ span(S1) ∩ span(S2)

  1. Jun 8, 2009 #1
    Hi! I wonder if you guys help me prove this:
    span(S1 ∩ S2) ⊆ span(S1) ∩ span(S2)
    I have seen span(S1 U S2) = span(S1) + span(S2), so I just want to prove this one, any suggestion?
  2. jcsd
  3. Jun 8, 2009 #2


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    Gold Member

    v=as, s in S1 and S2, thus v is in sp(S1) and sp(S2).
    Vice versa isn't necessarily because if v in sp(S1) and sp(S2), then v=as1=bs2, and s1 isn't necessarily in S2 and s2 isn't necessarily in S1.
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