# Linear System - Echelon Matrix

The Echelon form is a generalization of triangular matrices.

An

$m * n$

matrix A is in echelon form if it satisfies the following condition:

• for any row, if that row’s first nonzero entry is in position k
• then every previous row’s first nonzero entry is in some position less than k.

If a matrix is in echelon form, the nonzero rows form a basis for the row space