Answer
See below.
Work Step by Step
$T(a+b)=(a+b)''+a_1(a+b)'+a_2(a+b)=a''+b''+a_1a'+a_1b'+a_2a+a_2b=T(a)+T(b)$
$T(ca)=(ca)''+a_1(ca)'+a_2(ca)=c\cdot a''+c\cdot a_1a'+c\cdot a_2a=cT(a)$
Thus it is a linear transformation.
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 389: 3
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