Precalculus (10th Edition)

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

Chapter 11 - Systems of Equations and Inequalities - Chapter Review - Review Exercises - Page 794: 28

Answer

$-100.$

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 $D=2(0\cdot0-1\cdot6)-1(5\cdot0-1\cdot2)+(-3)(5\cdot6-0\cdot2)=2(-6)-1(-2)+(-3)(30)=-12+2-90=-100.$
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