$$\Delta = \left| {\matrix{ 3 & { - 2} & { - k} \cr 1 & { - 4} & { - 2} \cr 1 & 2 & { - 1} \cr } } \right| = 0$$

$$3(4 + 4) + 2( - 2 + 2) - k(4 + 4) = 0$$

$$ \Rightarrow k = 3$$

$${\Delta _x} = \left| {\matrix{ {10} & { - 2} & { - 3} \cr 6 & { - 4} & { - 2} \cr {5m} & 2 & { - 1} \cr } } \right| \ne 0$$

$$10(4 + 4) + 2( - 6 + 10m) - 3(12 + 20m) \ne 0$$

$$80 - 12 + 20m - 36 - 60m \ne 0$$

$$40m \ne 32 \Rightarrow m \ne {4 \over 5}$$

$${\Delta _y} = \left| {\matrix{ 3 & {10} & { - 3} \cr 2 & 6 & { - 2} \cr 1 & {5m} & { - 1} \cr } } \right| \ne 0$$

$$3( - 6 + 10m) - 10( - 2 + 2) - 3(10m - 6) \ne 0$$

$$ - 18 + 30m - 30m + 18 \ne 0 \Rightarrow 0$$

$${\Delta _z} = \left| {\matrix{ 3 & { - 2} & {10} \cr 2 & { - 4} & 6 \cr 1 & 2 & {5m} \cr } } \right| \ne 0$$

$$3( - 20m - 12) + 2(10m - 6) + 10(4 + 4) - 40m + 32 \ne 0 \Rightarrow m \ne {4 \over 5}$$