Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 4 - Vector Spaces - 4.5 Linear Dependence and Linear Independence - Problems - Page 297: 21


linearly independent.

Work Step by Step

If $ap_1(x)+bp_2(x)+cp_3(x)=a(1-3x^2)+b(2x+x^2)+5c=(5c+a)+(2b)x+(b-3a)x^2=0$, then $2b=0$, thus $b=0$, thus since $b-3a=0$, $a=0$, thus since $5c+a=0$, $c=0$, thus $a=b=0$, thus they are linearly independent.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.