|  |  |  |  |  |  |  |  |  |  |  | 
|  | Reduce column 1 with pivot 1 at row 2 |  |  |  |  |  |  |  |  |  | 
|  | Exchange row 1 and row 2 |  |  |  |  |  |  |  |  |  | 
|  |  |  |  |  |  |  |  |  |  |  | 
|  |  |  |  |  |  |  |  |  |  |  | 
|  |  |  |  |  |  |  |  |  |  |  | 
|  | Reduce column 2 with pivot 1 at row 3 |  |  |  |  |  |  |  |  |  | 
|  | Exchange row 2 and row 3 |  |  |  |  |  |  |  |  |  | 
|  |  |  |  |  |  |  |  |  |  |  | 
|  | | L3 <− (1)· L3−(−1)· L2  on |  | 
 |  |  |  |  |  |  |  |  |  | 
|  |  |  |  |  |  |  |  |  |  |  | 
|  | Reduce column 3 with pivot -4 at row 3 |  |  |  |  |  |  |  |  |  | 
|  | | L1 <− (1)· L1−(−3/4)· L3  on |  | 
 |  |  |  |  |  |  |  |  |  | 
|  | | L2 <− (1)· L2−(1/4)· L3  on | | ⎡ ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎣
 |  | ⎤ ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎦
 | 
 | 
 |  |  |  |  |  |  |  |  |  | 
|  | | End reduction | | ⎡ ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎣
 |  | ⎤ ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎦
 | 
 | 
 |  |  |  |  |  |  |  |  |  | 
|  |  |  |  |  |  |  |  |  |  |  | 
|  | Reduce column 1 with pivot 1 at row 2 |  |  |  |  |  |  |  |  |  | 
|  | Exchange row 1 and row 2 |  |  |  |  |  |  |  |  |  | 
|  | | L2 <− (1)· L2 −(2)· L1  on |  | 
 |  |  |  |  |  |  |  |  |  | 
|  |  |  |  |  |  |  |  |  |  |  | 
|  |  |  |  |  |  |  |  |  |  |  | 
|  | Reduce column 2 with pivot 1 at row 3 |  |  |  |  |  |  |  |  |  | 
|  | Exchange row 2 and row 3 |  |  |  |  |  |  |  |  |  | 
|  | | L1 <− (1)· L1 −(1)· L2  on |  | 
 |  |  |  |  |  |  |  |  |  | 
|  | | L3 <− (1)· L3−(−1)· L2  on |  | 
 |  |  |  |  |  |  |  |  |  | 
|  |  |  |  |  |  |  |  |  |  |  | 
|  | Reduce column 3 with pivot -4 at row 3 |  |  |  |  |  |  |  |  |  | 
|  | | L1 <− (1)· L1−(−3/4)· L3  on |  | 
 |  |  |  |  |  |  |  |  |  | 
|  | | L2 <− (1)· L2−(1/4)· L3  on | | ⎡ ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎣
 |  | ⎤ ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎦
 | 
 | 
 |  |  |  |  |  |  |  |  |  | 
|  | | End reduction | | ⎡ ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎢
 ⎣
 |  | ⎤ ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎥
 ⎦
 | 
 | 
 |  |  |  |  |  |  |  |  |  |