Chapter 2.3, Problem 3P

Explanation of Solution

Using Gauss-Jordan method to indicate the solutions:

Consider the given system of linear equations,

$\begin{array}{l}{x}_1+x_2=1\\ 2x_1+x_2=3\\ 3x_1+2x_2=4\end{array}$

The augmented matrix of this system is as follows:

$A|b=\left[\begin{array}{l}11\\ 21\\ 32\end{array}\right]\left[\begin{array}{l}1\\ 3\\ 4\end{array}\right]$

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 – 2 (row 1)), then the following matrix is obtained,

$A_1|b_1=\left[\begin{array}{l}11\\ 0-1\\ 32\end{array}\right]\left[\begin{array}{l}1\\ 1\\ 4\end{array}\right]$

Now, replace row 3 of $A_1|b_1$ by (row 3 – 3 (row 1)), then the following m