Algebra 58 - Gauss-Jordan Elimination with Dependent Systems 

This chapter builds on Algebra chapter 57 which explained the concept of dependency. In this chapter, we see that although it can sometimes be difficult to spot when a system of linear equations is dependent, when a dependent system is represented in matrix form and simplified through Gauss-Jordan elimination, an equivalent independent system is automatically produced. This equivalent system typically contains fewer equations, with fewer variables in each equation. From this simpler system, a parametric representation of the solution set can then be easily written.