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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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 29EQ
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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.
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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