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Can two subspaces have vectors in common

  1. Sep 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Can two 4-dimensional subspaces of F62 have exactly 9 vectors in common? Can they have exactly 8 vectors in common?

    F62 is the 6-dimensional field where each (a1, a2, a3, a4, a5, a6) is an element of F2.

    3. The attempt at a solution

    F62 obviously has 26 = 64 elements. I want to say that if each of the 4 vectors in both subspaces are the same, then there can be up to that are also the same, which would mean that 9 isn't possible, but I don't think that's right at all.

    Thank you ahead of time for your help.
     
  2. jcsd
  3. Sep 17, 2009 #2

    HallsofIvy

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    Well, if two subspace has any vectors in common, then they have the subspace spanned by those vector in common. How many vectors does a one-dimensional subspace contain?
     
  4. Sep 17, 2009 #3
    Just one (I would think)??
     
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