Ступенчатый вид матрицы

В линейной алгебре матрица считается приведенной к ступенчатому виду по строкам если

• All nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes, and
• The leading coefficient (the first nonzero number from the left, also called the pivot) of a nonzero row is always strictly to the right of the leading coefficient of the row above it.

This is an example of 3x4 matrix in row echelon form:

$\left[{\begin{array}{ccc|c}1&a_{1}&a_{2}&a_{3}\\0&4&a_{4}&a_{5}\\0&0&1&a_{6}\end{array}}\right]$