| ⎧ | 2x−y+4z=9 | |
| ⎨ | x+2y−2z=−9 | |
| ⎩ | 4x−4y−2z=27 |
| 1 | 9 | |||
1 − | 2 | | |||
| 2 | 2 |
| 1 | 9 | |||
1 − | 2 | | |||
| 2 | 2 |
| 5 | 27 | |||
0 | −4 | − | |||
| 2 | 2 |
| 5 | ||
w2 := w2/( | ) | |
| 2 |
| 1 | 9 | |||
1 − | 2 | | |||
| 2 | 2 |
| 8 | 27 | |||
0 1 − | | − | |||
| 5 | 5 |
| 1 | ||
w1 := w1 − (− | )*w2 | |
| 2 |
| 6 | 9 | |||
1 0 | | | |||
| 5 | 5 |
| 8 | 27 | |||
0 1 − | | − | |||
| 5 | 5 |
| 66 | 9 | |||
0 0 − | | − | |||
| 5 | 5 |
| 66 | ||
w3 := w3/(− | ) | |
| 5 |
| 6 | 9 | |||
1 0 | | | |||
| 5 | 5 |
| 8 | 27 | |||
0 1 − | | − | |||
| 5 | 5 |
| 3 | ||
0 0 1 | | ||
| 22 |
| 6 | ||
w1 := w1 − ( | )*w3 | |
| 5 |
| 8 | ||
w2 := w2 − (− | )*w3 | |
| 5 |
| 18 | ||
1 0 0 | | ||
| 11 |
| 57 | ||
0 1 0 | − | ||
| 11 |
| 3 | ||
0 0 1 | | ||
| 22 |