I'm trying to determine ifSis a basis forVifS={(1,2,1,0),(2,1,3,1),(2,2,1,2)} inV=spanS

so I made the matrix and put it in (not reduced) row echelon form which gives and this means that (1,2,1,0),(2,1,3,1) and (2,2,1,2) form a basis for and the dimension is 3.

I have a feeling I'm doing something wrong. Can someone tell me if this is right?