Chapter 2.2, Problem 30E

To determine

To fill:

The missing entries by performing the indicated row operations to obtain the row reduced matrix.

$\begin{array}{l}\left[\begin{array}{ccc}0& 1& 3\\ 1& 2& 1\\ 1& -2& 0\end{array}|\begin{array}{c}-4\\ 7\\ 1\end{array}\right]\stackrel{R_1\leftrightarrow R_2}{\to }\left[\begin{array}{ccc}\cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot \\ 1& -2& 0\end{array}|\begin{array}{c}\cdot \\ \cdot \\ 1\end{array}\right]\stackrel{R_3-R_1}{\to }\\ \left[\begin{array}{ccc}1& 2& 1\\ 0& 1& 3\\ \cdot & \cdot & \cdot \end{array}|\begin{array}{c}7\\ -4\\ \cdot \end{array}\right]\underset{R_3+4R_2}{\overset{R_1-2R_2}{\to }}\left[\begin{array}{ccc}\cdot & \cdot & \cdot \\ 0& 1& 3\\ \cdot & \cdot & \cdot \end{array}|\begin{array}{c}\cdot \\ -4\\ \cdot \end{array}\right]\stackrel{\frac{1}{11}{R}_3}{\to }\left[\begin{array}{ccc}1& 0& -5\\ 0& 1& 3\\ \cdot & \cdot & \cdot \end{array}|\begin{array}{c}15\\ -4\\ \cdot \end{array}\right]\\ \underset{R_2-3R_3}{\overset{R_1+5R_3}{\to }}\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}|\begin{array}{c}5\\ 2\\ -2\end{array}\right]\end{array}$