For inconsistent system of equation the conditions should be Δ=0 and at least one of the ΔxorΔyorΔz should not be equal to zero.
Now,
Δ=∣321−2−42−k−2−1∣=0
⇒24+2(0)−k(8)=0⇒k=3
And,
Δx=∣1065m−2−42−3−2−1∣
⇒Δx=[10(8)−2(−10m+6)−3(12+20m)]
⇒Δx=8(4−5m)
Δx=0⇒m=54
Δy=∣3211065m−3−2−1∣
=3(−6+10m)+10(0)−3(10m−6)
=0
Δz=∣321−2−421065m∣
⇒Δz=3(−20m−12)+2(10m−6)+10(4+4)
⇒Δz=−60m−36+20m−12+80
⇒Δz=−40m+32
⇒Δz=8(4−5m)
Δz=0⇒m=54