# What is the intuition behind the reduced row echelon form of a matrix?

When we convert a matrix into reduced row echelon form , the linearly independent vectors in the pivot columns form a unit vectors in the corresponding columns ? what is really happening here if I visualize it? we are performing row operations i.e operations on row vectors, so we are scaling down or up the row vectors by the same amount. But why this doesn't change the column vectors ?

• Row operations do not uniformly scale columns and they do change the column vectors. – Jim Jan 23 '15 at 6:13
• how does they change column vectors? – Tamim Addari Jan 24 '15 at 13:16
• They change the matrix. If your matrix is $\left[\begin{smallmatrix} 1 \\ 1 \end{smallmatrix}\right]$ then you can do a row operation and get $\left[\begin{smallmatrix} 1 \\ 0 \end{smallmatrix}\right]$, which is a different column vector. – Jim Jan 24 '15 at 17:46