Chapter 16.4, Problem 3E

To determine

To solve: given system by using an augmented matrix.

Answer to Problem 3E

There is one solution:

  $\begin{array}{l}x=1\\ y=-2\\ z=4\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}x-2y+z=9\\ 3x+y=1\\ -2x-3y-z=0\end{array}$

Calculation:

Write down the augmented matrix:

  $\left(\begin{array}{ccc}1& -2& 1\\ 3& 1& 0\\ 2& 3& 1\end{array}|\begin{array}{c}9\\ 1\\ 0\end{array}\right)$

Perform the Gauss-Jordan elimination,

  $\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}|\begin{array}{c}1\\ -2\\ 4\end{array}\right)$

As can be seen, there is one solution:

  $\begin{array}{l}x=1\\ y=-2\\ z=4\end{array}$