Title: Lecture 9: Direct Methods of Solving Linear Systems
Course: Numerical Analysis > Section: Module 5: Direct Methods for Solving Linear Systems

In this lecture we are going to study the Gauss elimination method to solve systems of linear equations. We first form an augmented matrix of the system. Then, using elementary row operations, we convert this matrix to an equivalent triangular matrix. We solve this matrix by back substitution.

We will also discuss partial pivoting aimed at reducing round-off errors. We will show how the use of elementary row operations can assist in determining both the determinant and the inverses of square matrices.

We will study yet another useful method of solving linear systems called the LU decomposition method.

Both these methods give an exact result subject to round-off errors. They do not, as many other numerical methods, provide approximate solutions that can be improved after further iterations. That is why they are called direct methods. However they use simple arithmetic calculations  to come to the solution, and hence we classify them too as numerical methods.