Answer
$$ - 0.051$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
{ - 0.3} & { - 0.1} & {0.9} \cr
{2.5} & {4.9} & { - 3.2} \cr
{ - 0.1} & {0.4} & {0.8} \cr
} } \right| \cr
& {\rm{Calculating\, the\, determinant \,by\, expanding \,the\, third\, column}} \cr
& \left| {\matrix{
{ - 0.3} & { - 0.1} & {0.9} \cr
{2.5} & {4.9} & { - 3.2} \cr
{ - 0.1} & {0.4} & {0.8} \cr
} } \right| = 0.9\left| {\matrix{
{2.5} & {4.9} \cr
{ - 0.1} & {0.4} \cr
} } \right| - \left( { - 3.2} \right)\left| {\matrix{
{ - 0.3} & { - 0.1} \cr
{ - 0.1} & {0.4} \cr
} } \right| \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + 0.8\left| {\matrix{
{ - 0.3} & { - 0.1} \cr
{2.5} & {4.9} \cr
} } \right| \cr
& {\rm{Solving}} \cr
& \left| {\matrix{
{ - 0.3} & { - 0.1} & {0.9} \cr
{2.5} & {4.9} & { - 3.2} \cr
{ - 0.1} & {0.4} & {0.8} \cr
} } \right| = 0.9\left( {1 + 0.49} \right) + 3.2\left( { - 0.12 - 0.01} \right)\, \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + 0.8\left( { - 1.47 + 0.25} \right) \cr
& {\rm{Simplifying}} \cr
& \left| {\matrix{
{ - 0.3} & { - 0.1} & {0.9} \cr
{2.5} & {4.9} & { - 3.2} \cr
{ - 0.1} & {0.4} & {0.8} \cr
} } \right| = 1.341 - 0.416 - 0.976 \cr
& \left| {\matrix{
{ - 0.3} & { - 0.1} & {0.9} \cr
{2.5} & {4.9} & { - 3.2} \cr
{ - 0.1} & {0.4} & {0.8} \cr
} } \right| = - 0.051 \cr} $$
