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: 12

Answer

$-24500.$

Work Step by Step

Since we have $$\left[\begin{array}{rrr} {40} & {25}&{10} \\ {30} & {5}&{20}\\{15}&{35}&{25}\end{array}\right]=5\left[\begin{array}{rrr} {8} & {5}&{2} \\ {6} & {1}&{4}\\{3}&{7}&{5}\end{array}\right]$$ then, we get $$\left|\begin{array}{rrr} {40} & {25}&{10} \\ {30} & {5}&{20}\\{15}&{35}&{25}\end{array}\right|=5^3\left|\begin{array}{rrr} {8} & {5}&{2} \\ {6} & {1}&{4}\\{3}&{7}&{5}\end{array}\right|=125(-196)=-24500.$$
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