What is the advantage of Gauss-Seidel's Method Gauss- Seidel's method is a technique to solve N linear equations in N unknowns, given an initial starting point. https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method
What are the advantages of using this method, when one can always find solutions using matrix inverse. 
 A: The computation of the inverse of a matrix is often not usable, e.g if one wants to solve linear systems of equations with say a million or even a billion of unknowns, that would be a very slow operation.
Often these very huge matrices have only very few nonzero elements,
in such cases one switches the strategie for solving from exact to approximate.
A prominent algorithm is the conjugate gradient method, see http://en.wikipedia.org/wiki/Conjugate_gradient_method, and its preconditioned variant. One or more steps of the Gauss Seidel method are often used for the preconditioned variant of the conjugate gradient method, as a means for that preconditioning.
The Gauss Seidel method and its cousin the Jacobi method, see http://en.wikipedia.org/wiki/Jacobi_method are basic algorithms, for the approximate solution of linear systems of equations, and they are used as building blocks for more complicated algorithms.
A: Gauss Siedel is computationally less intensive for large 'n' and has controlled round off error.
The inverse of the singular matrix does not exist. For that case, we will use the Gauss Siedel method for solving the system of linear Equations. 
