ABSTRACT
In this chapter, the authors find the solution of a system of linear equations. While this is an important topic in itself, the techniques the readers learn will carry over to many other types of problems. A system of linear equations that has either exactly one solution or infinitely many solutions is said to be consistent. A system of linear equations that has no solutions is inconsistent. The most common way of solving a system of linear equations is to convert the given system to an equivalent system where the solution to the equivalent system is obvious. By “an equivalent system” the readers mean that the two systems have the same variables and the same solution set. The manipulations of a system of equations that yield an equivalent system of equations have corresponding manipulations with the associated matrix. These manipulations correspond to multiplying the augmented matrix by particular elementary matrices.
