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 125: 8

Answer

$-250$

Work Step by Step

Since we have $$\left[\begin{array}{rrr} {5} & {15} \\ {10} & {-20}\end{array}\right]=5\left[\begin{array}{rrr} {1} & {3} \\ {2} & {-4}\end{array}\right]$$ then, we get $$\left|\begin{array}{rrr} {5} & {15} \\ {10} & {-20}\end{array}\right|=5^2\left|\begin{array}{rrr} {1} & {3} \\ {2} & {-4}\end{array}\right|=25(-4-6)=-250.$$
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