Answer
\[0\]
Work Step by Step
\[\begin{gathered}
{\text{Let }}A = \left| {\begin{array}{*{20}{c}}
{ - 1}&2&4 \\
4&{ - 8}&{ - 16} \\
0&0&0
\end{array}} \right| \hfill \\
{\text{Use the Determinant Theorem 1}}{\text{.}}\,\,\left( {{\text{See page 880}}} \right) \hfill \\
{\text{If every element in a row}}\left( {{\text{or column}}} \right){\text{of matrix }}A{\text{ is }}0,{\text{then}}\left| A \right| = 0 \hfill \\
{\text{In the third row all the elements are 0}}{\text{. Therefore,}} \hfill \\
A = \left| {\begin{array}{*{20}{c}}
1&0&0 \\
1&0&1 \\
3&0&0
\end{array}} \right| = 0 \hfill \\
\end{gathered} \]
