College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 8 - Section 8.3 - Systems of Linear Equations: Determinants - 8.3 Assess Your Understanding - Page 582: 43



Work Step by Step

We use one or a combination of theorems (11) to (15). --- Starting with $D=\left|\begin{array}{lll}{x}&{y}&{z}\\{u}&{v}&{w}\\{1}&{2}&{3}\end{array}\right|$, swapping rows 1 and 3, we obtain $D_{1}=\left|\begin{array}{lll}{1}&{2}&{3}\\{u}&{v}&{w}\\{x}&{y}&{z}\end{array}\right|$ By theorem (11), The value of a determinant changes sign if any two rows (or any two columns) are interchanged. $D_{1}=-D=-4$
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