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 - 4.4 Spanning Sets and Linear Independence - 4.4 Exercises - Page 178: 27


$S$ does not span $P_2$.

Work Step by Step

Since $x^2+2=2(1)+1(x^2)$, then $S=\{1,x^2,x^2+2\}$ is not linearly independent. But $P_2$ has the dimension $3$, $S$ does not span $P_2$. $S$ spans only a subspace of $P_2$, precisely, it spans the subspace of all polynomials on the form $p(x)=a+bx^2$
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