A system of linear Algebraic equations is nothing but a system of ' n' algebraic equations satisfied by a set of n unknown quantities. 

The aim is to find these n unknown quantities satisfying the n equations. 

It is a very common practice to write the system of n equations in matrix form as 

Ax = b  where A is an n x n, non-singular matrix and x and b are n x 1 matrices out of which b is known. 

For small n the elementary methods like cramers rule, matrix inversion are very convenient to get the unknown vector x from the system Ax = b. However, for large ' n ' these methods will become computationally very expensive because of the evaluation of matrix determinents involved in these methods. Hence to make the solution methods less expensive one has to find alternate means which doesn't require the evaluation of any determinents to find x form Ax = b . 

There are two types of methods exists to solve these linear systems. 
 

• Direct Methods

• Iterative methods