1. Not finding help here? Sign up for a free 30min 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!

Lin. Algebra - Sum of Dim. of Three Subspaces

  1. Feb 21, 2008 #1
    Another linear algebra question! What a surprise! :rolleyes:

    1. The problem statement, all variables and given/known data
    If U1, U2, U3, are subspaces of a finite-dimensional vector space, then show

    dim(U1 + U2 + U3) = dimU1 + dimU2 + dimU3 - dim(U1 [tex]\cap[/tex] U2) - dim(U1 [tex]\cap[/tex] U3) - dim(U2 [tex]\cap[/tex] U3) + dim(U1 [tex]\cap[/tex] U2 [tex]\cap[/tex] U3)

    or give a counterexample.

    2. Relevant equations



    3. The attempt at a solution
    I have the proof of the sum of the dimension of two subspaces in my book, so I would assume I would proceed in much the same way, but that "or give a counterexample" is making me just a little bit uneasy. I'm 90% sure that this is true, because basically the same formula holds for sets. Could anyone tell me if this is true before I proceed with my proof? It's gonna be a long one if I use the same method the book did.
     
  2. jcsd
  3. Feb 21, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    This has been asked more than once today, and I'll give you the same answer others have given. It is the same formula as for sets. And for the same reasons if you pick a compatible basis for the vector space. Proceed with your proof.
     
  4. Feb 22, 2008 #3
    Thanks for the response. I finished my proof, but where was this question asked earlier today? I didn't see it in the Homework Help or Linear Algebra forums.
     
  5. Feb 22, 2008 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Hmmm. Now I can't find it. It may be under an obscure title. BTW, I didn't mean to say that you should have searched for other posts before asking. I was only saying my response wasn't original.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Lin. Algebra - Sum of Dim. of Three Subspaces
Loading...