Answer
True
Work Step by Step
Given $rowspace (A) \ne R^n$. Thus, $A$ is not invertible.
Since $A$ and $B$ are row equivalent matrices, $B$ is not invertible also.
Hence, $colspace (B) \ne R^n$. 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 4 - Vector Spaces - 4.10 Invertible Matrix Theorem II - True-False Review - Page 332: e
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