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Homework Help: 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


    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 :)
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