Page 744 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 744
Thus, the number of operations required to complete successive steps is as follows:
Steps 1 and 1a.
Steps 2 and 2a.
Steps 3 and 3a.
Steps and a.
Step n.
Therefore, the total number of operations required to reduce to row-echelon form is
or, on applying Formulas 1 and 2,
(5)
(6)
This completes the operation count for the forward phase. For the backward phase we must put the row-echelon form of
into reduced row-echelon form by introducing zeros above the leading 1's. The operations are as follows:
