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. 5e7t - 6t 19 -5 x' = 60-18 e ; X₁ X₂² 12,7t 5e <- 6t 19 -5 5e7t ⠀⠀2 X₁ 60-18 12 e 7t 19 60-18

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...
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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.
- 6t
e
x' =
60 -
-5
X; x₁ =
18
5e7t
12 e 7t
x₂ =
5 e-6t
←
=X₁'
19
60 - 18
19 -5
60 - 18
5e7t
12e7t
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. - 6t e x' = 60 - -5 X; x₁ = 18 5e7t 12 e 7t x₂ = 5 e-6t ← =X₁' 19 60 - 18 19 -5 60 - 18 5e7t 12e7t
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