Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 6 - Linear Transformations - 6.3 The Kernel and Range of a Linear Transformation - Problems - Page 406: 14

Answer

See below

Work Step by Step

Consider the linear transformation $T : M_n(R) \rightarrow M_n(R)$, we have $Ker (T)=\{A \in M_n(R):T(A)=0\}\\ =\{A \in M_n(R):AB-BA=0\}\\ =\{A \in M_n(R):AB=BA\}$ Ker (T) is a set of matrices that commute with the matrix $B$
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