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First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system. -27 -31 -1 x' = 1 x x₁ = e X2 X3 24 28 -24 -24 3 =0=×₁' 4e-3t -27 -31 -1 24 28 1 3 -24 -24 -27-31 -1 24 28 1 3 H -24 -24

First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system. -27 -31 -1 x' = 1 x x₁ = e X2 X3 24 28 -24 -24 3 =0=×₁' 4e-3t -27 -31 -1 24 28 1 3 -24 -24 -27-31 -1 24 28 1 3 H -24 -24

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
Section2.5: Iterative Methods For Solving Linear Systems
Problem 5EQ
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First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system. -27-31 -1 x' = 24 28 |900 1 X; x₁ = e - 4 x₂ = 6 - 1 x3 = e 4 1 -27 - 31 5e-3t -1 24 28 - 3t =X₁' - 24 - 24 4e-3t - 24 - 24 3 - 27 - 31 -1 24 28 -24 -24 3 1 x₁ = 1 3 -4e C
Transcribed Image Text:First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system. -27-31 -1 x' = 24 28 |900 1 X; x₁ = e - 4 x₂ = 6 - 1 x3 = e 4 1 -27 - 31 5e-3t -1 24 28 - 3t =X₁' - 24 - 24 4e-3t - 24 - 24 3 - 27 - 31 -1 24 28 -24 -24 3 1 x₁ = 1 3 -4e C
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