Elementary Differential Equations and Boundary Value Problems 9th Edition

Published by Wiley
ISBN 10: 0-47038-334-8
ISBN 13: 978-0-47038-334-6

Chapter 4 - Higher Order Linear Equations - 4.1 General Theory of nth Order Linear Equations - Problems - Page 224: 9

Answer

$f_{1},f_{2},f_{3},f_{4}$ are linearly dependent.

Work Step by Step

$af_{1}(t)+bf_{2}(t)+cf_{3}(t)+df_{4}=\;a(2t-3)\;+b(t^2+1)\;+c(2t^2-t)\;+d(t^2+t+1)=\;0\\\\$ $(-3a+b+d)+\;(2a-c+d)t+(b+2c+d)t^2=0\\\\$ By the polynomial equality theorem: $\left\{\begin{matrix} -3a+b+d=0 \\ 2a-c+d=0 \\ b+2c+d=0 \end{matrix}\right. \rightarrow \;\;\;\;a=\frac{-2}{7}\;\;b=\frac{-13}{7}\;\;c=\frac{3}{7}\;\;c=\frac{3}{7}\;\;d=1\\\\$ so, $f_{1},f_{2},f_{3},f_{4}$ are linearly dependent.
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.