Linear Algebra, 5th Edition

3.1 Elementary Matrix Operations and Elementary Matrices

In this section, we define the elementary operations that are used throughout the chapter. In subsequent sections, we use these operations to obtain simple computational methods for determining the rank of a linear transformation and the solution of a system of linear equations. There are two types of elementary matrix operations—row operations and column operations. As we will see, the row operations are more useful. They arise from the three operations that can be used to eliminate variables in a system of linear equations.

Definitions.

Let A be an $m\times n$ matrix. Any one of the following three operations on the rows [columns] of A is called an elementary row [column] operation:

1. (1) interchanging ...