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!

Let V be a vector space

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose B = {u1, u2.. un} is a basis of V. Let U = {u1, u2...ui} and W = {ui+1, ui+2... un}. Prove that V = U ⊕ W.

    2. Relevant equations



    3. The attempt at a solution

    I think I should prove that elements in U are not in W and viceversa. Then this prove it is indeed a disjunction?
     
  2. jcsd
  3. Oct 23, 2012 #2
    Prove that if v is a nonzero vector in the intersection of U and W, then the u'is must be dependent.
     
  4. Oct 23, 2012 #3
    How can I show v is non zero?
     
  5. Oct 23, 2012 #4

    Mark44

    Staff: Mentor

    You assume that v is nonzero - that's what "if v is nonzero" means. You don't need to show the things that you are assuming.
     
  6. Oct 23, 2012 #5
    Thanks for the help guys :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook