The examples in previous chapters illustrate that solving linear programs involves the solution of systems of linear simultaneous algebraic equations. In this section we describe a method for solving a system of *n* linear equations in *n* unknowns that we use in subsequent sections. The method uses elementary row operations and corresponding elementary matrices. For a discussion of numerical issues involved in solving a system of simultaneous linear algebraic equations, we refer the reader to [41] and [53].

An elementary row operation on a given matrix is an algebraic manipulation of the matrix that corresponds to one of the following:

An elementary row operation on a matrix is equivalent to premultiplying the matrix by a corresponding *elementary matrix*, which we define next.

**Definition 16.1** We call ** E** an

An elementary matrix of the first kind formed from ** I** by interchanging the

Note that ** E** is invertible and

**Definition 16.2** We call ** E** an

Start Free Trial

No credit card required