ABSTRACT
This chapter builds on readers' familiarity with elementary functions, analytic geometry, and basic trigonometry to present matrices in a variety of algebraic and geometric settings. The central objects of study are systems of linear equations. The chapter shows that elementary row operations are appropriate for solving systems of linear equations. It compares the solution sets of two linear systems, where the augmented matrix of one system was obtained from the augmented matrix of the other by an elementary row operation and show that the solution sets are identical. The key to finding a solution of a complicated linear system is to find an equivalent system whose solution is obvious. Elementary row operations are the basic steps for the solution of linear systems. Two linear systems are equivalent if they have the same solutions. Two matrices are equivalent if one can be obtained from the other by a sequence of elementary row operations.
