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 - Problems - Page 419: 45

Answer

See below

Work Step by Step

$T:V \rightarrow W$ is a linear transformation with $\dim W=\dim [Rng(T)]=n$ and we have the fact that $Rng(T) \subseteq W$. Consequently, $T$ is onto.

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