Answer
True
Work Step by Step
We have $T:R^8 \rightarrow R^3$ is onto, then $Rng(T)=R^3\\
\rightarrow \dim [Rng(T)]=3$
Apply Rank Nullity Theorem:
$\dim [Ker(T)]+\dim [Rng(T)]=\dim R^8\\
\dim [Ker (T)]=5$
Hence, the statement is true.
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 417: l
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