Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 742: 14

$-119$

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 $D=3(4\cdot1-0\cdot(-3))-(-9)(1\cdot1-0\cdot8)+(4)(1\cdot(-3)-4\cdot8)=3(4)-(-9)(1)+(4)(-35)=12+9-140=-119.$