Page 30 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 30
Reducing roundoff errors
Minimizing the use of computer memory space
Solving the system with maximum speed
Some of these matters will be considered in Chapter 9. For hand computations, fractions are an annoyance that often cannot be
avoided. However, in some cases it is possible to avoid them by varying the elementary row operations in the right way. Thus, once
the methods of Gaussian elimination and Gauss–Jordan elimination have been mastered, the reader may wish to vary the steps in
specific problems to avoid fractions (see Exercise 18).
Remark Since Gauss–Jordan elimination avoids the use of back-substitution, it would seem that this method would be the more
efficient of the two methods we have considered.
It can be argued that this statement is true for solving small systems by hand since Gauss–Jordan elimination actually involves less
writing. However, for large systems of equations, it has been shown that the Gauss–Jordan elimination method requires about 50%
more operations than Gaussian elimination. This is an important consideration when one is working on computers.
Exercise Set 1.2
Click here for Just Ask!
Which of the following matrices are in reduced row-echelon form?
1.
(a)
(b)
(c)
(d)
(e)
