Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Skill Practice - Page 208: 24

$A_{ABC}=15$

$A(-4,6)$ $B(0, 3)$ $C(6, 6)$ $A_{ABC}=\pm\frac{1}{2}\begin{vmatrix} -4 & 6 & 1\\ 0 & 3 & 1 \\ 6 & 6 & 1 \end{vmatrix}$ $=\pm\frac{1}{2}[-4(3-6)-6(0-6)+1(0-18)]$ $=\pm\frac{1}{2}(12+36-18)$ $=\pm\frac{1}{2}.(30)$ $=\pm 15$ Hence $A_{ABC}=15$