Chapter 2.3, Problem 5P

Explanation of Solution

Using Gauss-Jordan method to indicate the solutions:

Consider the given system of linear equations,

$\begin{array}{l}{x}_1+x_4=5\\ x_2+2x_4=5\\ x_3+0.5x_4=1\\ 2x_3+x_4=3\end{array}$

The augmented matrix of this system is as follows:

$A|b=\left[\begin{array}{l}1001\\ 0102\\ 0010.5\\ 0021\end{array}\right]\left[\begin{array}{l}5\\ 5\\ 1\\ 3\end{array}\right]$

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