Answer
$dim[Rng(T)]=6$
Work Step by Step
Since $T$ is one-to-one, we can obtain:
$Ker(T)=\{0 \}=dim[Ker(T)]=0$
According to Rank-Nullity Theorem:
$dim[Ker(T)]+dim[Rng(T)]=dim[P_5(R)] \\
0+dim[Rng(T)]=6\\
dim[Rng(T)]=6$
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 - 6.6 Chapter Review - Additional Problems - Page 430: 17
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