Chapter 7.4, Problem 18E

To determine

To find:

Theaugmented matrix for the systems of linear equations.

Answer to Problem 18E

The augmented matrix is $\left(\begin{array}{ccc}1& -3& 1\\ 0& 4& 0\\ 0& 0& 7\end{array}|\begin{array}{l}1\\ 0\\ -5\end{array}\right)$ .

Explanation of Solution

Given information:

The system of equation is

  $\{\begin{array}{l}x-3y+z=1\\ 4y=0\\ 7z=-5\end{array}$

Steps for converting a system of equations in augmented matrix:

1.Write the coefficients of the $x$ terms as the numbers down the first column.

2.Write the coefficients of the $y$ terms as the numbers down the second column.

3.If there are $z$ terms, write the coefficients of the $z$ terms as the numbers down the third column.

4.Draw a vertical line and write the constants to the right of the line.

Rewrite the system of equation is as follows:

  $\{\begin{array}{l}x-3y+z=1\\ 0x+4y+0=0\\ 0x+0y+7z=-5\end{array}$

Follow the above steps and write the augmented matrix:

  $\left(\begin{array}{ccc}1& -3& 1\\ 0& 4& 0\\ 0& 0& 7\end{array}|\begin{array}{l}1\\ 0\\ -5\end{array}\right)$

Hence, augmented matrix is $\left(\begin{array}{ccc}1& -3& 1\\ 0& 4& 0\\ 0& 0& 7\end{array}|\begin{array}{l}1\\ 0\\ -5\end{array}\right)$ .