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: 16


It is not a vector space.

Work Step by Step

The set of all fifth-degree polynomials with the standard operationss is not a vector space because it is not closed under addition. For example, $f(x)=x^5$ and $g(x)=-x^5+x^2+1$. Now, $f(x)+g(x)=x^2+1$ which is a polynomial of degree $2$.
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