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 - 4.2 Vector Spaces - 4.2 Exercises - Page 160: 21


It is not a vector space.

Work Step by Step

The set $$\{(x, y) : x \geq 0, y \text { is a real number }\}$$ with the standard operations in $R^2$ is not a vector space because it is not closed under scalar multiplication. For example, $-2 (1,3)=(-2,-6)$ which is not in the set.
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