Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Skill Practice - Page 207: 16

$1728$

We know that for a matrix \[ \left[\begin{array}{rrr} a & b & c \\ d &e & f \\ g &h & i \\ \end{array} \right] \] the determinant is $D=a(ei-fh)-b(di-fg)+c(dh-eg).$ Hence here $D=-4(6\cdot0-0\cdot-12)-3(12\cdot0-0\cdot8)-9(12\cdot-12-6\cdot8)=-4(0)-3(0)-9(-192)=1728.$