##### Primary Goal

Solve a system of linear equations algebraically in parametric form.

Solve a system of linear equations algebraically in parametric form.

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