Gauss-Jordan Elimination

Just like the Gaussian Elimination, Gauss- jordan elimination aims to solve a system of linear equations. This is also done by transforming the system into augmented matrix, but the difference is, it needs to be a reduced row-echelon form.

Reduced Row-Echelon Form
- is basically a simpler form of a matrix. A matrix is in reduced row-echelon form if:

1. If there is a row where every entry is zero, then this row lies below any other row that contains a nonzero entry.
2. The leftmost nonzero entry of a row is equal to 1.
3. The leftmost nonzero entry of a row is the only nonzero entry in its column.
4. The nonzero entry on the higher row should be further to the left than the nonzero entry on the lower row.

     See that the final augmented matrix, the nonzero entries are in a staircase pattern. That means the equivalent linear equations are x=1, y=4 and z=-2 because it's the only nonzero entries in that row.