Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Skill Practice - Page 207: 15

$1160.$

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 $D=12(6\cdot4-(-8)\cdot10)-5(0\cdot4-(-8)\cdot1)+8(0\cdot10-6\cdot-1)=12(104)-5(8)+8(-6)=1160.$