Answer
See answer below
Work Step by Step
The vector $S$ has 4 independent elements
and we also have $dim (P_2(R))=3$
For $S$ to be a basis of $P_2(R)$, $S$ should have 3 independent elements.
Hence, $S$ is not a basis of $P_2(R)$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 4 - Vector Spaces - 4.6 Bases and Dimension - Problems - Page 309: 12
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