Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 3 - Determinants - 3.3 Properties of Determinants - 3.3 Exercises - Page 126: 62

Answer

$0$

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 $D=2(1\cdot2-2\cdot(-2))-(-1)((-3)\cdot2-2\cdot0)+(-1)((-3)\cdot(-2)-1\cdot0)=2(6)+1(-6)+(-1)(6)=12-6-6=0.$
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