Answer
$$ - 5.5$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
{0.4} & { - 0.8} & {0.6} \cr
{0.3} & {0.9} & {0.7} \cr
{3.1} & {4.1} & { - 2.8} \cr
} } \right| \cr
& {\rm{Calculating\, the\, determinant\, by\, expanding\, the\, third \,column}} \cr
& \left| {\matrix{
{0.4} & { - 0.8} & {0.6} \cr
{0.3} & {0.9} & {0.7} \cr
{3.1} & {4.1} & { - 2.8} \cr
} } \right| = 0.6\left| {\matrix{
{0.3} & {0.9} \cr
{3.1} & {4.1} \cr
} } \right| - 0.7\left| {\matrix{
{0.4} & { - 0.8} \cr
{3.1} & {4.1} \cr
} } \right| - 2.8\left| {\matrix{
{0.4} & { - 0.8} \cr
{0.3} & {0.9} \cr
} } \right| \cr
& {\rm{Solving}} \cr
& \left| {\matrix{
{0.4} & { - 0.8} & {0.6} \cr
{0.3} & {0.9} & {0.7} \cr
{3.1} & {4.1} & { - 2.8} \cr
} } \right| = 0.6\left( {1.23 - 2.79} \right) - 0.7\left( {1.64 + 2.48} \right) - 2.8\left( {0.36 + 0.24} \right) \cr
& {\rm{Simplifying}} \cr
& \left| {\matrix{
{0.4} & { - 0.8} & {0.6} \cr
{0.3} & {0.9} & {0.7} \cr
{3.1} & {4.1} & { - 2.8} \cr
} } \right| = - 0.936 - 2.884 - 1.68 \cr
& \left| {\matrix{
{0.4} & { - 0.8} & {0.6} \cr
{0.3} & {0.9} & {0.7} \cr
{3.1} & {4.1} & { - 2.8} \cr
} } \right| = - 5.5 \cr} $$
