I am trying to explain why S is not a basis for R3.

S={(1,1,2),(0,2,1)}

S is a basis if it spans and is linearly independent.

I have determined that S is linearly independent from c1(1,1,2)+c2(0,2,1)=0;c1=c2=0

The next step is to determine if it spans. I can't use the determinant since it is not a square matrix. Could someone help me how to determine if a non-square matrix spans or not?