# Elementary Row Operations - only need two?

1. Jan 19, 2009

### clg211

I was reading that the "exchange rows" operation can be achieved through the other two operations: multiplication by a nonzero number and adding a multiple of one row to another.

Any thoughts on the actual algorithm for achieving an exchange of rows through these other two operations? I realize it should be an iterative process, but not sure where it would start.

2. Jan 19, 2009

### Hurkyl

Staff Emeritus
I would start with the elementary matrix for a swap, and try and reduce it to row echelon form using only adds and multiplies.

$$\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}$$