Chapter 2, Problem 7RP

Explanation of Solution

Using Gauss-Jordan method to indicate the solutions:

Consider the given system of linear equations,

$\begin{array}{l}2x_1+x_2=3\\ 3x_1+x_2=4\\ x_1-x_2=0\end{array}$

The augmented matrix of this system is as follows:

$A|b=\left[\begin{array}{l}21\\ 31\\ 1-1\end{array}\right]\left[\begin{array}{l}3\\ 4\\ 0\end{array}\right]$

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

$A_1|b_1=\left[\begin{array}{l}21\\ 0-1\\ 1-1\end{array}\right]\left[\begin{array}{l}3\\ -1\\ 0\end{array}\right]$

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