Gaussian elimination

Gaussian elimination, sometimes called simpy elimination, is a method in mathematics that is used to solve a system of linear equations. Such sets of equations occur throughout mathematics, physics, and even in the optimization of business practices, such as scheduling of bus routes, airlines, trains, and optimization of profits as a function of supplies and sales. The method can be accomplished using written equations, but is more often simplified using matrix forms of the equations.

Three basic manuevers are allowed in the Gaussian elimination method:

1. Interchanging any two equations
2. Multiplying both sides of any equation by a non-zero number
3. Adding a multiple of one equation to another equation