Gauss Jordan Elimination

Gauss Jordan elimination

Its a new version of Gaussian elimination, which puts zeros till we have an diagonal matrix. 

Solving linear equations this method we obtain:

-->The solution of the equations. 
-->The matrix inverse.

Are you wondering the difference between Gauss Jordan and Gaussian elimination?

The difference is "Back substitution" the idea is to take a diagonal matrix and operate it on reverse order.

At the end we will have the rows of the matrix in echelon form, the diagonal will have ones and in the right side the solution vector. 

For instance:

Let's see example showed in Gaussian Elimination.

Written like a matrix:

 

At this point we have the upper triangular matrix: 

Next step is "BACK SUBSTITUTION". At the end we will get the matrix in the next form:

Inmediatly we can note that:

X = 3

Y = 1

Z = 2