Chapter 2.3, Problem 6P

Explanation of Solution

Using Gauss-Jordan method to indicate the solutions:

Consider the given system of linear equations,

$\begin{array}{l}2x_2+2x_3=4\\ x_1+2x_2+x_3=4\\ x_2-x_3=0\end{array}$

The augmented matrix of this system is as follows:

$A|b=\left[\begin{array}{l}022\\ 121\\ 01-1\end{array}\right]\left[\begin{array}{l}4\\ 4\\ 0\end{array}\right]$

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

Replace row 2 of A|b by (row 2 – row 1), then the following matrix is obtained,