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 - 3.3 Cofactor Expansions - True-False Review - Page 231: c

Answer

False

Work Step by Step

According to Definition 3.3.1, if we look at any $n x n$ diagonal matrix $A$, we can see that for $i=j$, minor will be determinal of a diagonal matrix obtained by removing the $i-th$ row and $i-th$ column vectors of A. The product of diagonal sequence is the determinant of the diagonal matrix, according to Theorem 3.2.1. We have $M_{ii}=a_{11}a_{12}...a_{i-1}a_{i+1}...a_{nn}$ The statement is false since minor is one number, not a matrix.
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