Chapter 9 - Polar Coordinates; Vectors - 9.7 The Cross Product - 9.7 Assess Your Understanding - Page 631: 14

$10A+2B+2C.$

We know that for a matrix \[ \left[\begin{array}{rrr} a & b & c \\ d &e & f \\ g &h & i \\ \end{array} \right] \] the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$ Hence here $D=A((-2)\cdot(-2)-(-3)\cdot2)-B(1\cdot(-2)-(-3)\cdot0)+C(1\cdot2-(-2)\cdot0)=10A+2B+2C.$