Chapter 2.3, Problem 7P

Explanation of Solution

Using Gauss-Jordan method to indicate the solutions:

Consider the given system of linear equations,

$\begin{array}{l}{x}_1+x_2=2\\ -x_2+2x_3=3\\ x_2+x_3=3\end{array}$

The augmented matrix of this system is as follows:

$A|b=\left[\begin{array}{l}110\\ 0-12\\ 011\end{array}\right]\left[\begin{array}{l}2\\ 3\\ 3\end{array}\right]$

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 2), then the following matrix is obtained,

$A_1|b_1=\left[\begin{array}{l}110\\ 0-12\\ 003\end{array}\right]\left[\begin{array}{l}2\\ 3\\ 6\end{array}\right]$

Now, replace row 1 of $A_1|b_1$ by (row 1 + row 2), then the following matrix is obtained,

$A_2|b_2=\left[\begin{array}{l}102\\ 0-12\\ 003\end{array}\right]\left[\begin{array}{l}5\\ 3\\ 6\end{array}\right]$

Now, replace row 2 of $A_2|b_2$ by (– 1(row 2)), then the following matrix is obtained,