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Math Help - Spanning Sequences of subspace

  1. #1
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    Spanning Sequences of subspace

    How do i find a spanning sequences of a subspace. IE. {(x, y, z) E(Belongs to ) R^3 : 2x + y -3z=0}
    I can prove it is a subspace but i need the spanning sequence.
    Any help is appriciated Thanks
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  2. #2
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    Re: Spanning Sequences of subspace

    You can choose y and z arbitrarily and then determine x. So, choose (x1, 1, 0) and (x2, 0, 1) for appropriate x1 and x2.
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  3. #3
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    Re: Spanning Sequences of subspace

    Any vector (x, y, z), in this subspace satisfies 2x+ y- 3z= 0 or y= 3z- 2x. That is any such vector is of the form < x, 3z- 2x, z>= <x, -2x, 0>+ <0, 3z, z>= x<1, -2, 0>+ z<0, 3, 1>. Can you see what a basis must be?
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