Gauss-Jordan Method

Gauss-Jordan Elimination A method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations. Example: x + y + z = 5 2x + 3y + 5z = 8 4x + 5z = 2 Solution: The augmented matrix of the system is the following. 1 1 1     5 2 3 5     8 4 0 5     2 1 0 0     a 0 0 1     b      [WERE  abc are Real Numbers] 0 0 0     c We will now perform row operations until we obtain a matrix in reduced row echelon form.   1 1 1 5 2 3 5 8 4 0 5 2   R2−2R1 −−−−−→   1 1 1 5 0 1 3 −2 4 0 5 2   R3−4R1 −−−−−→   1 1 1 5 0 1 3 −2 0 −4 1 −18   R3+4R2 −−−−−→   1 1 1 5 0 1 3 −2 0 0 13 −26   1 13R3 −−−→   1 1 1 5 0 1 3 −2 0 0 1 −2   R2−3R3 −−−−−→   1 1 1 5 0 1 0 4 0 0 1 −2   R1−R3 −−−−→   1 1 0 7 0 1 0 4 0 0 1 −2   R1−R2 −−−−→   1 0 0 3 0 1 0 4 0 0 1 −2  