# Math Help - finding a basis from set of vectors

1. ## 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]
$
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]
$
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?

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