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Math Help - finding a basis from set of vectors

  1. #1
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    finding a basis from set of vectors

    I'm trying to determine if S is a basis for V if S={(1,2,1,0),(2,1,3,1),(2,2,1,2)} in V=spanS

    so I made the matrix \left[ \begin{array}{cccc} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 1 & 3 & 1 \\ 0 & 1 & 2 \end{array} \right]<br />
and put it in (not reduced) row echelon form which gives \left[ \begin{array}{cccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0  \end{array} \right]<br />
and this means that (1,2,1,0),(2,1,3,1) and (2,2,1,2) form a basis for R^4 and the dimension is 3.
    I have a feeling I'm doing something wrong. Can someone tell me if this is right?
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  2. #2
    MHF Contributor

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    Yes, you are right- those three vectors are independent and so form a basis for their span.
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