Answer
See below
Work Step by Step
We know $A$ is an $n × n$ matrix, then
$B+C=\frac{1}{2}(A+A^T)+\frac{1}{2}(A-A^T)=\frac{1}{2}A^T+\frac{1}{2}A^T+\frac{1}{2}A-\frac{1}{2}A^T=A$
Thus, $A=B+C$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 2 - Matrices and Systems of Linear Equations - 2.2 Matrix Algebra - Problems - Page 137: 33
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