The reduced row echelon form of a matrix is the row echelon form (see previous section) with 0s above the leading 1s in each row. Gauss-Jordan reduction will turn any matrix into reduced row echelon form, and the reduced row echelon form of a matrix is unique. If the matrix is the augmented matrix of a system, then the reduced row echelon form of the matrix is the simplest form to solve the system. The rref command finds the reduced row echelon form of a matrix (see also Section 6.34.17).
Examples.
| ⎧ ⎨ ⎩ |
|
| ⎡ ⎢ ⎣ |
| ⎤ ⎥ ⎦ |
| ⎧ ⎨ ⎩ |
|
| ⎧ ⎨ ⎩ |
|
| ⎡ ⎢ ⎣ |
| ⎤ ⎥ ⎦ |
| ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ |