Answer
0
Work Step by Step
$$\eqalign{
& \left| {\matrix{
1 & { - 2} & 3 \cr
0 & 0 & 0 \cr
1 & {10} & { - 12} \cr
} } \right| \cr
& {\rm{Calculating\, the\, determinant\, by\, expanding\, the \,second\, row}} \cr
& \left| {\matrix{
1 & { - 2} & 3 \cr
0 & 0 & 0 \cr
1 & {10} & { - 12} \cr
} } \right| = - 0\left| {\matrix{
{ - 2} & 3 \cr
{10} & { - 12} \cr
} } \right| + 0\left| {\matrix{
1 & 3 \cr
1 & { - 12} \cr
} } \right| - 0\left| {\matrix{
1 & { - 2} \cr
1 & {10} \cr
} } \right| \cr
& {\rm{Solving}} \cr
& \left| {\matrix{
1 & { - 2} & 3 \cr
0 & 0 & 0 \cr
1 & {10} & { - 12} \cr
} } \right| = 0 \cr} $$
