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 - 6.1 Definition of a Linear Transformation - Problems - Page 390: 39

Answer

See below

Work Step by Step

Let $T_1(v)=Av \\ T_2(v)=Bv$ with $v \in R^n$ Then we have $(T_1+T_2)v=T_1(v)+T_2(v)\\ =Av+Bv\\ =(A+B)v$ Hence $T_1+T_2$ is the linear transformation given by $A+B$ We obtain $(cT_1)v=cT_1(v)=cAv=$ with $v \in R^n$ Hence $cT_1$ is the linear transformation given by $cA$

Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.