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: 68


$A$ is symmetric.

Work Step by Step

Let the matrix $A$ be given by $$A=\left[\begin{array}{ccc}{2} &{1} \\{1}& {3} \end{array}\right].$$ Since Since $a_{ij}=a_{ji}$ for all $i,j$, then $A$ is symmetric. Also, this can be shown by the fact that $$A^T=\left[\begin{array}{ccc}{2} &{1} \\{1}& {3} \end{array}\right] =A.$$
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