We will now discuss an algebraic method of moving from one basic feasible solution to another until the optimal solution is found. We will then streamline this process by introducing and using matrix methods. An important feature of this method is this it will not require us to find all the basic solutions of (2) or even all the basic feasible solutions. Instead we will only have to find a subset of the basic feasible solutions. To start, we write (1) in the following initial from: