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Homework Help: Can someone help me with this proof?

  1. Feb 20, 2007 #1
    1. The problem statement, all variables and given/known data

    Can someone help me with this proof? I'm supposed to show that if a subspace S is contained in subspace V, then S perp contains V perp.

    2. Relevant equations

    None, or the dimensions must add up, so S + S perp = some dimension N, and V + V perp equals the same dimension N, if S and V are both subspaces of N.

    3. The attempt at a solution

    Am I supposed to show that the dimensions don't add up? Can anyone provide suggestions? Thanks.
  2. jcsd
  3. Feb 20, 2007 #2


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    S perp contains V perp iff x in V perp implies x in S perp.
    x in V perp iff for all y in V, <x,y> = 0.
    x in S perp iff for all y in S, <x,y> = 0.

    So you want to show (for all y in V, <x,y> = 0) implies (for all y in S, <x,y> = 0). Well S is a subset of V, so this is obvious.
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