Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 2 - Matrices - 2.2 Properties of Matrix Operations - 2.2 Exercises - Page 61: 70


Since $$A^T=\left[\begin{array}{ccc}{0}&{-2} &{1} \\{2}&{0}& {3}\\{-1}&{-3}&{0} \end{array}\right] =-A,$$ then $A$ is skew-symmetric.

Work Step by Step

Let the matrix $A$ be given by $$A=\left[\begin{array}{ccc}{0}&{2} &{-1} \\{-2}&{0}& {-3}\\{1}&{3}&{0} \end{array}\right].$$ Since $$A^T=\left[\begin{array}{ccc}{0}&{-2} &{1} \\{2}&{0}& {3}\\{-1}&{-3}&{0} \end{array}\right] =-A,$$ then $A$ is skew-symmetric.
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