Chapter 2, Problem 10RP

Explanation of Solution

Using Gauss-Jordan method to indicate the solutions:

Consider the given system of linear equations,

$\begin{array}{l}{x}_1-x_3=4\\ x_2+x_3=2\\ x_1+x_2=5\end{array}$

The augmented matrix of this system is as follows:

$A|b=\left[\begin{array}{l}10-1\\ 011\\ 110\end{array}\right]\left[\begin{array}{l}4\\ 2\\ 5\end{array}\right]$

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,

$A_1|b_1=[\begin{array}{l}10-1\\ 0\end{array}$