Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 10


$W$ is not a vector subspace of $R^2$.

Work Step by Step

Let $u=(1,2)\in W$, so the components of $u$ are integer but the vector $\frac{1}{2}u=\frac{1}{2}(1,2)=(\frac{1}{2},1)$ has components which are not integer. Hence $W$ is not vector subspace of $R^2$.
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