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Te X, = ( E. Arc there any valucs I where the vectors X1 and 2e 2c arc not lincarly independent? (Answ: Yes, r = 2 and -2.)

Te X, = ( E. Arc there any valucs I where the vectors X1 and 2e 2c arc not lincarly independent? (Answ: Yes, r = 2 and -2.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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E. Are there any values \( x \) where the vectors \( \vec{X_1} = \begin{pmatrix} xe^x \\ 2e^x \end{pmatrix} \) and \( \vec{X_2} = \begin{pmatrix} 2e^x \\ xe^x \end{pmatrix} \) are not linearly independent? (Answer: Yes, \( x = 2 \) and \( -2 \).)
Transcribed Image Text:E. Are there any values \( x \) where the vectors \( \vec{X_1} = \begin{pmatrix} xe^x \\ 2e^x \end{pmatrix} \) and \( \vec{X_2} = \begin{pmatrix} 2e^x \\ xe^x \end{pmatrix} \) are not linearly independent? (Answer: Yes, \( x = 2 \) and \( -2 \).)
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