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 - 2.7 Elementary Matrices and the LU Factorization - True-False Review - Page 186: d

Answer

See below

Work Step by Step

The rank of a matrix is not changed when performing an elementary row operation on it. Then, by performing the elementary row operation associated with the elementary matrix $E$, the matrix $EA$ can be obtained from $A$. As a result, $EA$ and $A$ are on the same level. Hence, the statement is true.
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