In this course we will be exploring a wide variety of topics related to vectors and matrices. We will see that nearly everything we discuss reduces, in one way or another, to solving a system of linear equations. The purpose of this chapter is to provide the tools necessary for solving these systems. In fact, there is rather a lot that one can say about systems of linear equations. We will say more in future chapters; for now, our goal is just to develop enough machinery to facilitate the calculations that arise in the examples in Chapter 2.