Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 742: 9

$-2$

We know that for a matrix \[ \left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right] \] the determinant is $D=ad-bc.$ Hence, here we have $D=(-3\cdot2)-(-1\cdot4)\\ D=-6-(-4)\\ D=-6+4\\ D=-2$