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 198: 4

Answer

A line in $R^2$ that does not pass through the origin is not closed under vector addition. See image below

Work Step by Step

See image. Vectors $\vec{u}_1$ and $\vec{u}_2$ are on the line and therefore in the vector space, but their sum, $\vec{u}_1+\vec{u}_2$ is not.
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