Answer
$$50$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
8 & { - 2} & { - 4} \cr
7 & 0 & 3 \cr
5 & { - 1} & 2 \cr
} } \right| \cr
& {\rm{Calculating\, the\, determinant \,by\, expanding \,the \,second\, row}} \cr
& \left| {\matrix{
8 & { - 2} & { - 4} \cr
7 & 0 & 3 \cr
5 & { - 1} & 2 \cr
} } \right| = - 7\left| {\matrix{
{ - 2} & { - 4} \cr
{ - 1} & 2 \cr
} } \right| + 0\left| {\matrix{
8 & { - 4} \cr
5 & 2 \cr
} } \right| - 3\left| {\matrix{
8 & { - 2} \cr
5 & { - 1} \cr
} } \right| \cr
& {\rm{Solving}} \cr
& \left| {\matrix{
8 & { - 2} & { - 4} \cr
7 & 0 & 3 \cr
5 & { - 1} & 2 \cr
} } \right| = - 7\left( { - 4 - 4} \right) + 0 - 3\left( { - 8 + 10} \right) \cr
& {\rm{Simplifying}} \cr
& \left| {\matrix{
8 & { - 2} & { - 4} \cr
7 & 0 & 3 \cr
5 & { - 1} & 2 \cr
} } \right| = 50 \cr} $$
