Question Number 104759 by mohammad17 last updated on 23/Jul/20
Answered by bobhans last updated on 24/Jul/20
$${vol}\:=\:\frac{\mathrm{1}}{\mathrm{6}}\left(\mid\:\:{det}\begin{pmatrix}{\mathrm{1}\:\:\:\:\:−\mathrm{1}\:\:\:\:\:\:\:\mathrm{4}}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{pmatrix}\:\mid\right) \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{6}}\mid\mathrm{1}.\left(−\mathrm{2}\right)−\left(−\mathrm{1}\right)\left(\mathrm{6}\right)+\mathrm{4}\left(\mathrm{4}\right)\:\mid\: \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{6}}\left(−\mathrm{2}+\mathrm{6}+\mathrm{16}\right)\:=\:\frac{\mathrm{10}}{\mathrm{3}}\:\blacksquare\: \\ $$