The problem

This presentation is devoted to solving linear systems of the form

The unknowns are and they need to satisfy simultaneously all equations. Several simulaneous equations form a system; each equation is linear (involves only the first power of the unknowns), therefore we have a linear system of equations. The numbers are called the coefficients ( is the coefficient of variable in equation number ) and are called the right hand sides.

Linear systems arise in a variety of applications in science and engineering.