Answer
$$17$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
1 & 2 & 0 \cr
{ - 1} & 2 & { - 1} \cr
0 & 1 & 4 \cr
} } \right| \cr
& {\rm{Calculating\, the \,determinant \,by \,expanding\, the \,third\, row}} \cr
& \left| {\matrix{
1 & 2 & 0 \cr
{ - 1} & 2 & { - 1} \cr
0 & 1 & 4 \cr
} } \right| = 0\left| {\matrix{
2 & 0 \cr
2 & { - 1} \cr
} } \right| - \left| {\matrix{
1 & 0 \cr
{ - 1} & 1 \cr
} } \right| + 4\left| {\matrix{
1 & 2 \cr
{ - 1} & 2 \cr
} } \right| \cr
& {\rm{Solving}} \cr
& \left| {\matrix{
1 & 2 & 0 \cr
{ - 1} & 2 & { - 1} \cr
0 & 1 & 4 \cr
} } \right| = 0 - \left( 1 \right) + 4\left( {2 + 2} \right) \cr
& {\rm{Simplifying}} \cr
& \left| {\matrix{
1 & 2 & 0 \cr
{ - 1} & 2 & { - 1} \cr
0 & 1 & 4 \cr
} } \right| = 17 \cr} $$
