Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 3 - Determinants - 3.1 The Definition of the Determinant - Problems - Page 206: 10


Yes, even, plus sign

Work Step by Step

We have an entry from each column and each row thus it is a determinant of order $5$. The ordered pairs that are out of order are(if we swap $a_{32}$ and $a_{24}$ it is easier to see it): $(4,2),(4,3),(5,4),(3,2)$, thus the number of inversions is $2$, the parity is even, thus the sign is positive.
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