Illustration of gauss-jordan elimination:
An illustration of interchanging rows would be r1 ¬→ r3, that would results:
Now, beginning with this matrix, an illustration of scaling would be: 2r2 → r_{2}, that means all the elements in row 2 are multiplied by 2. These results:
Now, beginning with this matrix, an illustration of a replacement would be: r_{3} - 2r_{2} → r_{3}. Element-by-element, row 3 is substituted by the element in row 3 minus 2 * the equivalent element in row 2. This result:
Both the Gauss and Gauss-Jordan techniques start with the matrix form Ax = b of a system of equations, and then augment the coefficient matrix A with the column vector b.