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

$10$

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 $D=3((-1)\cdot(-2)-5\cdot2)-4(1\cdot(-2)-5\cdot1)+2(1\cdot2-(-1)\cdot1)=3(-8)-4(-7)+2(3)=-24+28+6=10.$