The way you understood it wrong
When I was doing engineering, I had a very good algebra teacher.* Those were the days full of vectors and subspaces and subspaces of polynomials and matrices and subspaces of matrices of polynomials. All from 7 a.m to 12 p.m. In the middle of that math trench he said once something that my head really saved. The teacher was explaining yet another concept while the sky was still dark in the morning and there was this guy that asked him to clarify a detail. ...