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Math Help - Linearly dependency and coplanarity of vectors

  1. #1
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    Linearly dependency and coplanarity of vectors

    the question is:

    is this set of vectors coplanar?
    (1,-1,1),(0,1,1),(1,0,2)

    I am getting an answer of no because I am finding that a+b+c=0 but only if a=b=c=0
    and they that would not make them linearly dependent, thus not coplanar

    i did a(1,-1,1)+b(0,1,1+c(1,0,2)=0
    I went on to try to solve for each letter always coming up with a=b=c=0

    the correct answer should be yes they are coplanar though
    Last edited by colorado; January 18th 2011 at 10:24 AM. Reason: added info
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    For example:

    r\begin{bmatrix}{1}&{-1}&{1}\\{0}&{1}&{1}\\{1}&{0}&{2}\end{bmatrix}=2

    So, the rows generate a subspace W such that \dim W=2 (plane).


    Fernando Revilla
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