College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 6 - Summary, Review, and Test - Review Exercises - Page 657: 48

Answer

$-62.$

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 $D=2(-1\cdot0-5\cdot4)-4(1\cdot0-5\cdot(-2))+(-3)(1\cdot4-(-1)\cdot(-2))=2\cdot(-2)-4\cdot10+(-3)\cdot6=-4-40-18=-62.$
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