Chapter 2.3, Problem 4P

Explanation of Solution

Indicating the solutions using Gauss-Jordan method:

Consider the following system of equations.

$\begin{array}{c}2x_1-x_2+x_3+x_4=6\\ x_1+x_2+x_3=4\end{array}$

The augmented matrix of this system is given below:

$A|b=\left(\begin{array}{ccccc}2& -1& 1& 1& 6\\ 1& 1& 1& 0& 4\end{array}\right)$

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

Replacing row 2 by row 1 of $A|b$, we get

$A_1|b_1=\left(\begin{array}{ccccc}1& 1& 1& 0& 4\\ 2& -1& 1& 1& 6\end{array}\right)$

Now, replace row 2 of $A_1|b_1$ by (row 2 of $A_1|b_1$) – 2(row 1 of $$