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 - 6.1 Definition of a Linear Transformation - Problems - Page 389: 13

Answer

See below

Work Step by Step

Take $A \in M_2(R)\\ c \in R$ $T: M_2(R)\rightarrow R$ defined by $T(A)=\det (A)$ We obtain: $$T(c(A))=\det(A)=c^2A\\ cT(A)=cA\\ \rightarrow T(c(A))\ne cT(A)$$ Thus it is not a linear transformation.
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