Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 742: 12

$-169.$

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 $D=1(1\cdot3-(-5)\cdot2)-3(6\cdot3-(-5)\cdot8)+(-2)(6\cdot2-1\cdot8)=1(13)-3(58)+(-2)(4)=13-174-8=-169.$