Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Skill Practice - Page 207: 17

$-480$

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 $D=-2(15\cdot7-3\cdot-1)-6(8\cdot7-3\cdot4)+0(8\cdot-1-15\cdot4)=-2(108)-6(44)+0(-68)=-480.$