The Gauss-Jordan elimination

Gauss-Jordan elimination is a systematic method used to solve systems of linear equations. It works by transforming a matrix representing the equations into a simplified form called reduced row echelon form. This involves using row operations—like swapping, multiplying, or adding rows—to create zeros below and above pivots (leading non-zero numbers in each row). Once in this form, the solutions to the equations become clear and can be read directly. Essentially, it's a step-by-step process to isolate each variable, making complex systems easier to solve efficiently and accurately.