Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.7 The Cross Product - 8.7 Assess Your Understanding - Page 651: 14

Answer

$10A+2B +2C$

Work Step by Step

The determinant for a $3 \times 3$ matrix can be found as: $det = \begin{vmatrix} a & b & c \\ d &e & f \\ g &h & i \\ \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$ As per the problem, $det=\begin{vmatrix} A & B & C \\ 1 & -2 & -3 \\ 0 & 2 & -2 \\ \end{vmatrix}\\=A[(-2)(-2)-(-3)(2)]-B((1)(-2)- (-3) (0)]+C[(1)(2)- (-2) (0)] \\=10A+2B +2C$
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