1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor

    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)??
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook