Definition of (echelon matrix/matrix in (row) echelon form)

Definition: A matrix is in row echelon form if:

1. All nonzero rows are above any rows of all zeros.
2. The leading entry (first nonzero entry from the left, also called the pivot) of each nonzero row is in a column to the right of the leading entry of the row above it.
3. All entries in a column below a leading entry are zeros.

Example (in echelon form):
$$\begin{pmatrix} \boxed{2} & 3 & 1 \\ 0 & \boxed{4} & 5 \\ 0 & 0 & \boxed{6} \end{pmatrix}$$

Note: Some definitions additionally require the leading entry to be 1, but this is not universal. When leading entries are all 1 and are the only nonzero entries in their column, the matrix is in reduced row echelon form.