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 6 - Linear Transformations - 6.4 Additional Properties of Linear Transformation - Problems - Page 419: 39

Answer

See below

Work Step by Step

Let $u$ be arbitrary vectors in $U$, and let $c$ be a scalar. We obtain: $(T_2T_1)(cu_1)=T_2(T_1(cu_1))\\ =T_2(cT_1(u_1))\\ =cT_2(T_1(u_1))\\ =c(T_2T_1)(u_1)$

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