An algorithm that uses simple row operations to bring a matrix into row-echelon form.
Steps:
- optional: Pull out any scalars from each row in the matrix.
- If the first entry in the first row is
, swap it with another row that has a non-zero entry in its first column. Otherwise, move to step 3. - Multiply through the first row by a scalar to make the leading entry equal to
. - Add scaled multiples of the first row to every other row in the matrix until every entry of the first column, other than the leading
in the first row, is a . - Go back to step 2 and repeat the process until the matrix is in reduced row-echelon form.