Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Skill Practice - Page 207: 18

$-260.$

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 $D=5(0\cdot7-8\cdot8)-7(-4\cdot7-8\cdot1)+6(-4\cdot8-0\cdot1)=5(-64)-7(-36)+6(-32)=-260.$