Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 9 - Polar Coordinates; Vectors - 9.7 The Cross Product - 9.7 Assess Your Understanding - Page 631: 11

Answer

$-11A+2B+5C.$

Work Step by Step

We know that for a matrix \[ \left[\begin{array}{rrr} a & b & c \\ d &e & f \\ g &h & i \\ \end{array} \right] \] the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$ Hence here $D=A(1\cdot1-4\cdot3)-B(2\cdot1-4\cdot1)+C(2\cdot3-1\cdot1)=-11A+2B+5C.$
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