\begin{align} \left| A \right| &= 1 \\ A^{-1} &= \begin{pmatrix} 21 & -8 & -11 \\ -2 & 1 & 1 \\ -11 & 4 & 6 \end{pmatrix} \end{align}
\begin{align} \mathrm{div} \boldsymbol{f} = 2x+2z \end{align} なので、 \begin{align} \iiint_V \mathrm{div} \boldsymbol{f} \ dV &= 2 \iiint_V (x+z) \ dV \\ &= 2 \int_0^1 dy \int_0^3 dz \int_0^{3-z} dx \ (x+z) \\ &= 2 \int_0^3 dz \left[ \frac{x^2}{2} + xz \right]_{x=0}^{x=3-z} \\ &= \int_0^3 dz \ \left( -z^2 + 9 \right) \\ &= 18 \end{align} を得る。