By systematically eliminating variables, this algorithm efficiently finds the unknown values in multiple interconnected linear equations.

This descending staircase pattern isolates one variable per row, allowing mathematicians to easily solve the system from the bottom up.

The method was detailed in the ancient Chinese text The Nine Chapters on the Mathematical Art over a millennium before Gauss was born.

These valid mathematical operations include swapping rows, multiplying a row by a constant, and adding a multiple of one row to another.