# Solving systems of equations using Jordan exchanges

## Homework Statement:

solve the following system of equations

## Homework Equations:

$B_ij = A_{ij} - (A_{rj}/A_{rs})(A_{is})$
$B_{ir} = A_{is}/A_{rs}$
2u + 3v + 3w = 2
+ 5v + 7w = 2
6u + 9v + 8w = 5

$\begin{bmatrix} 2 & 3 & 3 & 2 \\ 0 & 5 & 7 & 2 \\ 6 & 9 & 8 & 5 \end{bmatrix}$

We have been asked to use Jordan exchange to solve the above equations. Can someone please explain how to determine the values for r, s for the equations above. I believe r is the row number of the dependent variable chosen to be switched with the column for the independent variable, being s. For example, if row 3 and column 3 are chosen, then s = 3 and r = 3. These positions are then used in the homework equations above. Thanks in advance!