What happened to the last row? But what you have done is correct, so far. If you were to complete the row reduction you would have, as reduced echelon form,
so that your basis vectors are <1, 0 , 0>, <0, 1, 0>, and <0, 0, 1>, the standard basis for . That is because this matrix maps into and its null space has dimension 1 so its image is all of .