Page 742 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

row-echelon form. This assumption is justified by the fact that row interchanges are performed as bookkeeping operations on a
computer (that is, they are simulated, not actually performed) and so require much less time than arithmetic operations.

Since no row interchanges are required, the first step in the Gauss–Jordan elimination process is to introduce a leading 1 in the first
row by multiplying the elements in that row by the reciprocal of the leftmost entry in the row. We shall represent this step
schematically as follows:

Note that the leading 1 is simply recorded and requires no computation; only the remaining n entries in the first row must be
computed.

The following is a schematic description of the steps and the number of operations required to reduce to row-echelon form.

Step 1.

Step 1a.

Step 2.

Step 2a.