Linear Algebra and Its Applications (5th Edition)

by Lay, David C.; Lay, Steven R.; McDonald, Judi J.

Published by Pearson

ISBN 10: 032198238X

ISBN 13: 978-0-32198-238-4

Chapter 2 - Matrix Algebra - 2.8 Exercises - Page 153: 3

Answer

See image and solution

Work Step by Step

The set is not closed under sums or scalar multiples. For example, Vectors u and v are in H, but their sum, u+v is not in H. Therefore, H is not a subspace of $R^2$. Also, although vector u is in H, vector -3u is not.

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