The given vectors are solutions of a system X' = AX. Determine whether the vectors form a fundamental set on the interval (-00, 0). e-2t, X, = e-7t O Yes, since the set X,, X, is linearly independent for -00
The given vectors are solutions of a system X' = AX. Determine whether the vectors form a fundamental set on the interval (-00, 0). e-2t, X, = e-7t O Yes, since the set X,, X, is linearly independent for -00
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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Intro to Diff Equation I
![The given vectors are solutions of a system X' = AX. Determine whether the vectors form a fundamental set on the interval (-00, 0).
e-2t, X2 =
e-7t
O Yes, since the set X,, X, is linearly independent for -0 <t < o.
O Yes, since the set X,, X, is linearly dependent for -00 < t < ∞.
O No, since the set X,, X, is linearly independent for -∞ < t < o.
O No, since the set X,, X, is linearly dependent for -00 < t < ∞,
O There is not enough information.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F061326ef-a001-4812-8db1-40a0883f09dc%2Fe463ed7b-b13d-4d81-a665-3493f8ef2cb4%2Fadn2teg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The given vectors are solutions of a system X' = AX. Determine whether the vectors form a fundamental set on the interval (-00, 0).
e-2t, X2 =
e-7t
O Yes, since the set X,, X, is linearly independent for -0 <t < o.
O Yes, since the set X,, X, is linearly dependent for -00 < t < ∞.
O No, since the set X,, X, is linearly independent for -∞ < t < o.
O No, since the set X,, X, is linearly dependent for -00 < t < ∞,
O There is not enough information.
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