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 - 2.9 Chapter Review - Additional Problems - Page 192: 11

Answer

See below

Work Step by Step

Let $A$ be an $m \times n$ matrix and let $B$ be an $p\times n$ matrix. Then, (j,i) entry of $AB^T=\sum^n_{k=0}a_{jk}b^T_{ki}=\sum^n_{k=0}a_{jk}b+{ik}=\sum^n_{k=0}b_{ik}a_{kj}^T$ Hence, the (i,j)-entries of $(AB^T)^T$ and $BA^T$ are the same.
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