| | | | | | | | | | |
| 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 | ⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣ | | ⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦ |
|
| | | | | | | | | |