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 - Review Exercises - Page 139: 43


(a) $$|ِAB|= 8.$$ (b) $$|B^2|= 4.$$ (c) $$|2A|= 64.$$ (d) $$|(AB)^T|=8.$$ (e) $$|B^{-1}|=\frac{1}{2}.$$

Work Step by Step

(a) $$|ِAB|=|A||B|=(4)(2)=8.$$ (b) $$|B^2|=|B|^2=2^2=4.$$ (c) $$|2A|=2^4|A|=(16)(4)=64.$$ (d) $$|(AB)^T|=|B^TA^T|=|B^T||A^T|=|B||A|=(2)(4)=8.$$ (e) $$|B^{-1}|=|B|^{-1}=\frac{1}{2}.$$
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