Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Skill Practice - Page 208: 22

$A_{ABC}=6$

$A(1, 5)$ $B(4, 6)$ $C(7, 3)$ $A_{ABC}=\frac{1}{2}\begin{vmatrix} 1 & 5 & 1\\ 4 & 6 & 1 \\ 7 & 3 & 1 \end{vmatrix}$ $=\frac{1}{2}[1(6-3)-5(4-7)+1(12-42)]$ $=\frac{1}{2}(3+15-30)$ $=\frac{1}{2}.(-12)$ $=-6$ Hence $A_{ABC}=6$