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, Problem 1RP

Explanation of Solution

Using Gauss-Jordan method to indicate the solutions:

Consider the given system of linear equations,

x1+x2=2x2+x3=3x1+2x2+x3=5

The augmented matrix of this system is as follows:

A|b=[1 1 00 1 11 2 1][235]

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 1), then the following matrix is obtained,

A1|b1=[1 1 00 1 10 1 1][233]

Now, replace row 3 of A1|b1 by (row 3 - row 2), then the following matrix is obtained,

A2|b2=[1 1 00 1 10 0 0][230]

This produces the following result,

x1+x2=2x2+x3=3

Solving the above equations, the following result is obtained,

x1=k1x2=3kx3=k

Therefore, the above system of linear equations has a unique solution.

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