Gauss-Jordan Elimination

Next we have to discuss elementary row operations. There are three of them & we will give both the notation utilized for each one as well as an instance using the augmented matrix given above.

1.   Interchange Two Rows. Along with this operation we will interchange all the entries in row I and row j. The notation we'll use here is R_i  ↔ R _j .   Following is an example.

Thus, we do accurately what the operation says.  In the third row every entry moves up to the first row & each entry in the first row moves down to the third row.  Ensure that you move all the entries.  One of the more common errors is to forget to move one or more entries.