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: 34

Answer

is a vector space.

Work Step by Step

Since the sum of two continuous functions is continuous and also the multiplication of continuous by a scalar is continuous. Then all other conditions for the vector space can be checked very easily. Hence, the set of all continuous functions $C[-1,1]$ defined on the interval $[-1,1]$ with the standard operation is a vector space.
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