Definition:Echelon Matrix/Reduced Echelon Form

Definition
Let $\mathbf A = \sqbrk a_{m n}$ be a matrix in echelon form whose order is $m \times n$.

The matrix $\mathbf A$ is in reduced echelon form, in addition to being in echelon form, the leading $1$ in any non-zero row is the only non-zero element in the column in which that $1$ occurs.

Such a matrix is called a reduced echelon matrix.