Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Chapter 2.3, Problem 7P

Explanation of Solution

Using Gauss-Jordan method to indicate the solutions:

Consider the given system of linear equations,

x1+x2=2x2+2x3=3x2+x3=3

The augmented matrix of this system is as follows:

A|b=[1 1 00 -1 20 1 1][233]

The Gauss-Jordan method is applied to find the solutions of the above system of linear equations.

Replace row 3 of A|b by (row 3 + row 2), then the following matrix is obtained,

A1|b1=[1 1 00 -1 20 0 3][236]

Now, replace row 1 of A1|b1 by (row 1 + row 2), then the following matrix is obtained,

A2|b2=[1 0 20 -1 20 0 3][536]

Now, replace row 2 of A2|b2 by (– 1(row 2)), then the following matrix is obtained,

A3|b3=[1 0 20 1 -20 <

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