Answer
\[168\]
Work Step by Step
\[\begin{gathered}
{\text{Let }}A = \left| {\begin{array}{*{20}{c}}
7&0&0 \\
1&6&0 \\
4&2&4
\end{array}} \right| \hfill \\
{\text{Use the Determinant Theorem 7}}{\text{.}}\,\,\left( {{\text{See page 880}}} \right) \hfill \\
{\text{If matrix }}A{\text{ is in triangular form}},{\text{ having only zeros either above or }} \hfill \\
{\text{below the main diagonal}},{\text{ then}}\,\left| A \right|{\text{is the product of the elements on }} \hfill \\
{\text{the main diagonal of }}A.\,{\text{Therefore,}} \hfill \\
A = \left| {\begin{array}{*{20}{c}}
7&0&0 \\
1&6&0 \\
4&2&4
\end{array}} \right| = \left( 7 \right)\left( 6 \right)\left( 4 \right) = 168 \hfill \\
\end{gathered} \]
