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Math Help - Subspaces help!

  1. #1
    Newbie
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    Sep 2008
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    6

    Post Subspaces help!

    Let W be a subset of R^3 with elements (x,y,z) that satisfy:

    a1x + a2y + a3z = 0
    b1x + b2y + b3z= 0

    for some ai and bj with at least one ai and one bj non-zero. Prove that W is a subspace of R^3. Find the dimension of W if:

    a) a1/ b1 = a2/ b2 = a3/ b3

    b) if all the above proportions are not equal.
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    If the two equations are not the same, then W is a line, and if they are the same, then W is a plane.
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