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