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: 10

Answer

$2304$

Work Step by Step

Since we have $$\left[\begin{array}{rrr} {4} & {16}&{0} \\ {12} & {-8}&{8}\\{16}&{20}&{-4}\end{array}\right]=4\left[\begin{array}{rrr} {1} & {4}&{0} \\ {3} & {-2}&{2}\\{4}&{5}&{-1}\end{array}\right]=4\left[\begin{array}{rrr} {1} & {4}&{0} \\ {11} & {8}&{0}\\{4}&{5}&{-1}\end{array}\right]$$ then, we get $$\left|\begin{array}{rrr} {4} & {16}&{0} \\ {12} & {-8}&{8}\\{16}&{20}&{-4}\end{array}\right|=4^3\left|\begin{array}{rrr} {1} & {4}&{0} \\ {11} & {8}&{0}\\{4}&{5}&{-1}\end{array}\right|=64(-1)(8-44)=2304.$$
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