Chapter 16.4, Problem 1E

To determine

To solve: given system by using an augmented matrix.

Answer to Problem 1E

There is one solution:

  $x=5,y=-1,z=-4$ .

Explanation of Solution

Given information:

  $\begin{array}{l}x+y+z=0\\ x-y+z=2\\ x-y-z=10\end{array}$

Calculation:

Write down the augmented matrix:

  $\left(\begin{array}{ccc}1& 1& 1\\ 1& -1& 1\\ 1& -1& -1\end{array}|\begin{array}{c}0\\ 2\\ 10\end{array}\right)$

Perform the Gauss-Jordan elimination,

  $\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}|\begin{array}{c}5\\ -1\\ -4\end{array}\right)$

As can be seen, there is one solution: $x=5,y=-1,z=-4$ .