Gauss Jordan Elimination

A direct numerical method for evaluating a given linear system of equations

It is an alternate version of the Gauss elimination. It asks the user the augmented matrix to be evaluated. It scales the coefficients and the constants so that the largest coefficient is 1. The purpose of scaling is to minimize round-off errors, especially when one of the equations has a relatively larger coefficient than the rest, and to also thoroughly check for ill-conditioned systems. It also employs partial pivoting, where the current pivot equation is replaced if its pivot element is near 0. Partial pivoting is applied through the whole computational process and so not just only once (if such is necessary). When all other equations have a pivot element near 0, it alerts the user. It also alerts the user if the system is either an ill-conditioned system or a singular system.