Answer
False
Work Step by Step
For the linear transformation $T : C^1[a, b] \rightarrow C^0[a, b]$ we obtain:
$Ker (T)=\{f \in C^1[a,b]: T(f)-0\}\\
=\{f \in C^1[a,b]: f'=0\}\\
=\{c:c \in R\} \ne \{0\}$
Hence, $T(f)=f'$ is not one-to-one.
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 - True-False Review - Page 416: g
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