1. ## Matrices - Elimination

Hi,
What is the difference between elementary row operations, Gaussian Elimination, and Gauss-Jordan Elimination?
I am confused between these 3 concepts.

For operations on rows on augmented matrices using elem. row operations, they said:
1. Multiply a row through by a nonzero constant
2. Interchange 2 rows
3. Add a multiple of one row to another
Their example wasn't clear to me though, so I don't understand the steps for that.

2. Elementary Row Operations: Gaussian Elemination

$\displaystyle\begin{bmatrix}5&7\\1&12\end{bmatrix} \Rightarrow\mbox{Change row 1 with 2}\begin{bmatrix}1&12\\5&7\end{bmatrix}\Rightarrow \mbox{-5R1+R2}\begin{bmatrix}1&12\\0&-53\end{bmatrix}\Rightarrow\mbox{1/-53*R2}\begin{bmatrix}1&12\\0&1\end{bmatrix}$

Get the idea?

3. Gauss Jordan

$\displaystyle\begin{bmatrix}1&12\\0&1\end{bmatrix} \Rightarrow\mbox{R1-12R2}\begin{bmatrix}1&0\\0&1\end{bmatrix}$

4. Thanks.