Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 4 - Vector Spaces - 4.1 Exercises - Page 199: 30

Answer

See solution

Work Step by Step

Let us suppose $c\vec{u}=\vec{0}$. Then, $c\vec{u}+c\vec{u}=\vec{0}+\vec{0}=\vec{0}$, which means $c(\vec{u}+\vec{u})=\vec{0}=c\vec{u}$ using axiom 7. Then, $\vec{u}+\vec{u}=2\vec{u}=\vec{u}$, which can only be true if $\vec{u}$ is the zero vector
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