### Abstract:

In thesis we present an iterative method to solve a system of equations
approximately. Firstly we use two iterative methods for the solutions of a
system of algebraic equations namely Gauss Jacobi iteration method and
Gauss-Siedel iteration method. Most the iterative methods may converge
or not. However certain class of systems of simultaneous equations which
is diagonally dominant do always converge to a solution using Gauss-Siedel
method. It is possible that a system of equation might be diagonally dominant
if we exchanges the equations with each other.
Also, we presented the singular value decomposition(SVD). It has been
used to determine the properties of matrix, matrix norm and rank. Since
the inverse of a matrix is often di cult to compute accurately,the SVD is
used to compute the matrix inverse and then solving a linear systems of
equations.
Also, we use the SVD method to solve one of the least squares problems
which is overdetermined problem. We use the MATLAB software for the
solution.