Chapter 2, Problem 4RP

Explanation of Solution

Using Gauss-Jordan method to indicate the solutions:

Consider the given system of linear equations,

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

The augmented matrix of this system is as follows:

$A|b=\left[\begin{array}{l}23\\ 11\\ 12\end{array}\right]\left[\begin{array}{l}3\\ 1\\ 2\end{array}\right]$

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

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

$A_1|b_1=\left[\begin{array}{l}23\\ 0-1\\ 12\end{array}\right]\left[\begin{array}{l}3\\ -1\\ 2\end{array}\right]$

Now, replace row 3 of $A_1|b_1$ by 2(row 3) - row 1, then the following matrix is obtained,

$$