Differential Equations and Linear Algebra (4th Edition)

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

Chapter 2 - Matrices and Systems of Linear Equations - 2.1 Matrices: Definitions and Notation - Problems - Page 122: 33

Answer

See below

Work Step by Step

$A$ is a $n\times n$ skew- symmetric matrix then $a_{ij}=a_{ji}$ (according to symmetric property) and $a_{ij}=-a_{ji}$ (skew-symmetric property) It follows that $a_{ij}=a_{ji}=-a_{ji}\\ \rightarrow a_{ji}=-a_{ji}$ The only possibility for this kind of matrix is with all zero elements. Hence, $A$ is a zero matrix.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.