Answer
$$166$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
{10} & 2 & 1 \cr
{ - 1} & 4 & 3 \cr
{ - 3} & 8 & {10} \cr
} } \right| \cr
& {\rm{Calculating\, the\, determinant\, by\, expanding\, the \,second\, row}} \cr
& \left| {\matrix{
{10} & 2 & 1 \cr
{ - 1} & 4 & 3 \cr
{ - 3} & 8 & {10} \cr
} } \right| = 1\left| {\matrix{
2 & 1 \cr
8 & {10} \cr
} } \right| + 4\left| {\matrix{
{10} & 1 \cr
{ - 3} & {10} \cr
} } \right| - 3\left| {\matrix{
{10} & 2 \cr
{ - 3} & 8 \cr
} } \right| \cr
& {\rm{Solving}} \cr
& \left| {\matrix{
{10} & 2 & 1 \cr
{ - 1} & 4 & 3 \cr
{ - 3} & 8 & {10} \cr
} } \right| = \left( {20 - 8} \right) + 4\left( {100 + 3} \right) - 3\left( {80 + 6} \right) \cr
& {\rm{Simplifying}} \cr
& \left| {\matrix{
{10} & 2 & 1 \cr
{ - 1} & 4 & 3 \cr
{ - 3} & 8 & {10} \cr
} } \right| = 166 \cr} $$
