Chapter 10 - Systems of Equations and Inequalities - Section 10.3 Systems of Linear Equations: Determinants - 10.3 Assess Your Understanding - Page 760: 14

$-119$

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, $D=3 [(4) (1) -(-3)(0)]+9(1)(1)-(8)(0)]+4[(1)(-3)-(8)(4)]\\=(3)(4) +(9)(1)+(4)(-35) \\=12+9-140 \\=-119$