This chapter is devoted to the algebraic study of systems of linear equations and their solutions. We will learn a systematic way of solving equations of the form

In Section 2.1, we will introduce systems of linear equations, the class of equations whose study forms the subject of linear algebra. In Section 2.2, will present a procedure, called row reduction, for finding all solutions of a system of linear equations. In Section 2.3, you will see how to express all solutions of a system of linear equations in a unique way using the parametric form of the general solution. Finally, in Section 2.4, we will learn how to write a system of linear equations succinctly as a matrix equation, which looks like where is an matrix, is a vector in and is a variable vector in