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: 20


It is not a vector space.

Work Step by Step

The set of all quadratic functions whose graphs pass through the origin with the standard operations is not a vector space because it is not closed under addition. For example, $f(x)=x^2+x$ and $g(x)=-x^2+2x$ are two quadratic functions passing through the origin but $f(x)+g(x)=3x$ which is not quadratic.
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