Example

Let S=span{Transpose[1 0 1], Transpose[0 1 1], Transpose[1 1 2], Transpose[1 2 1], Transpose[-1 1 2]} be a subspace of R^3.


  Clear[a,m]
  a={{1,0,1,1,-1},{0,1,1,2,1},{1,1,2,1,2}};
  MatrixForm[a]


  m=RowReduce[Transpose[a]];
  MatrixForm[m]


  MatrixForm[Transpose[m]]

So, the standard basis for S is actually the standard unit vector basis for R^3, that is, S=R^3.