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Subspace prove question

  1. Mar 4, 2009 #1
    V is a vector space on feild F and there is a series[tex]v=(v_1,v_2,v_3,v_4)[/tex]
    which is independent on V
    W_1=sp(v1,v2)
    W_2=sp(v2,v3)
    of V
    prove that
    [tex]
    W_1\cap W_2=sp(v2)
    [/tex]
    its obvious v2 exists in both groups .
    how am i supposed to prove it
    ??
     
  2. jcsd
  3. Mar 4, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Since
    [itex]W_1\cap W_2[/itex] is a subspace of W1, and W1 has dimension 2, it has dimension 1 or 2. If it has dimension 2, the it is equal to W2. But W_1 contains v1 which is not in [itex]W_1\cap W_2[/itex] so it is not of dimension 2.
     
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