Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Skill Practice - Page 208: 28

Answer

Answer A

Work Step by Step

$A(-3,4)$ $B(6, 3)$ $C(2, -1)$ $A_{ABC}=\pm\frac{1}{2}\begin{vmatrix} -3 &4 & 1\\ 6 & 3 & 1 \\ 2 & -1 & 1 \end{vmatrix}$ $=\pm\frac{1}{2}[-3(3+1)-4(6-2)+1(-6-6)]$ $=\pm\frac{1}{2}(-12-16-12)$ $=\pm\frac{1}{2}.(-40)$ $=\pm(-20)$ Hence $A_{ABC}=20$. The correct answer is A.
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