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: 44

Answer

a) $$|ِAB|= -10.$$ (b) $$|B^4| =625.$$ (c) $$|2A|= -16.$$ (d) $$|(AB)^T|= -10.$$ (e) $$|B^{-1}|= \frac{1}{5}.$$

Work Step by Step

(a) $$|ِAB|=|A||B|=(-2)(5)=-10.$$ (b) $$|B^4|=|B|^4=5^4=625.$$ (c) $$|2A|=2^3|A|=(8)(-2)=-16.$$ (d) $$|(AB)^T|=|B^TA^T|=|B^T||A^T|=|B||A|=(5)(-2)=-10.$$ (e) $$|B^{-1}|=|B|^{-1}=\frac{1}{5}.$$
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