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Math Help - column space for this vector space

  1. #1
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    column space for this vector space

    Problem is find a basis and its dimension.
    Let W={(a,b,c):a-3b+c=0, b-2c=0, 2b-c=0}. I know that W=Nul A and it can be set up as
    [1 -3 1][a]=[0]
    [0 1 -2][b]=[0]
    [0 2 -1][c]=[0]

    when row reduced it turns out to be
    [1 0 0][a]=[0]
    [0 1 0][b]=[0]
    [0 0 1][c]=[0]

    The Nul A={0} and there exists no basis for it so the dimension is 0 but what about a basis for the column space. Wouldn't its dimension be 3 and a basis be
    {(1 0 0),(-3 1 2),(0 2 -1)}? I can see it might be a basis since the only vector in W is (0 0 0).
    Last edited by bonfire09; December 18th 2012 at 09:57 AM.
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: column space for this vector space

    A Basis for a vector space is a set of linearly independent vectors which span the vector space. Now, the vector space W only contains  0_w . So does not have a basis and  Dim(W) = 0 .
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