Determine whether the members of the given set of vectors are linearly independent for -o < t < o. If they are linearly dependent, find a linear relation among them. x"(t) x(t) = 3et 2e 2e-t e The vectors are linearly independent. x = Choose one Choose one -2x(1) + 4x2) + x' x(3) = 0 x(1) – x(2) + 4x(3) = 0 - %3D -2x(4) + 4x(2) – x(3) x(4) – x(2) + x(3) -

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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linear independence of vectors 

Determine whether the members of the given set of vectors are
linearly independent for -0o < t <o. If they are linearly dependent,
find a linear relation among them.
x"(t)
3e t
x(t) =
x(2)
2e
2e-t
e
The vectors are linearly independent.
x = Choose one
Choose one
-2x(1) + 4x(2)
x(3)
= 0
x(1) – x(2) + 4x(3) = 0
-
%3D
-2x(4) + 4x(2) – x(3)
x(4) – x(2) + x(3)
-
Transcribed Image Text:Determine whether the members of the given set of vectors are linearly independent for -0o < t <o. If they are linearly dependent, find a linear relation among them. x"(t) 3e t x(t) = x(2) 2e 2e-t e The vectors are linearly independent. x = Choose one Choose one -2x(1) + 4x(2) x(3) = 0 x(1) – x(2) + 4x(3) = 0 - %3D -2x(4) + 4x(2) – x(3) x(4) – x(2) + x(3) -
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