Chapter 10 - Systems of Equations and Inequalities - Section 10.3 Systems of Linear Equations: Determinants - 10.3 Assess Your Understanding - Page 760: 13

$-26$

The determinant for a 3 by 3 matrix can be computed as: $Determinant (D)= \begin{vmatrix} A & B & C \\ a & b & c \\ g &h & i \\ \end{vmatrix}=A(ei-fh)-B(di-fg)+C(dh-eg)$ Therefore, $D=4 [(-1) (4) -(0)(-3)]+1[(6)(4)-(1)(0)]+(2)[(6)(-3)-(1)(-1)]\\=(4)(-4) +1(24)+(2)(-17) \\=-16+24-34 \\=-26$