Answer
$n=1764$
Work Step by Step
Since $T$ is an isomorphism, we can obtain:
$dimV=dimW$
According to Rank-Nullity Theorem:
$dim[M_{42}(R)]=dim[R^n] \\
=42^2\\
=1764
\rightarrow n=1764$
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: 18
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