Answer
See answer below
Work Step by Step
Since $rowspace (A)=nullspace (A) \rightarrow rank (A)=nullity (A)$
Hence, $rank (A)+nullity (A)$ is even.
Since $rank (A)+nullity (A)$ is number of columns of $A$, $A$ contains an even number of columns.
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 4 - Vector Spaces - 4.9 The Rank-Nullity Theorem - Problems - Page 330: 16
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