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First verify that hie independent. Finally, write the general solution of the system. 19 - 12 3. 11t x' = = e X2 = e -11t 20 - 19 19 - 12 X1 20 - 19 19 - 12 3e 11t 20 - 19 2e 11t 19 - 12 X2 20 - 19 19 %3D 2e-11t - 12 20 - 19 5e-11t The Wronskian of the solutions is W= Are the solutions linearly independent? O Yes O No The general solution is x(t) =.

First verify that hie independent. Finally, write the general solution of the system. 19 - 12 3. 11t x' = = e X2 = e -11t 20 - 19 19 - 12 X1 20 - 19 19 - 12 3e 11t 20 - 19 2e 11t 19 - 12 X2 20 - 19 19 %3D 2e-11t - 12 20 - 19 5e-11t The Wronskian of the solutions is W= Are the solutions linearly independent? O Yes O No The general solution is x(t) =.

Elementary Linear Algebra (MindTap Course List)
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.
 
x′=
  19 −12  
20 −19
x​;
x1=e11t
  3  
2
​,
x2=e−11t
  2  
5
  19 −12  
20 −19
x1=
  19 −12  
20 −19
•
  3e11t  
2e11t
=nothing=x1′
  19 −12  
20 −19
x2=
  19 −12  
20 −19
•
  2e−11t  
5e−11t
=nothing=x2′
The Wronskian of the solutions is
W=nothing.
Are the solutions linearly​ independent?
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 systen. 19 -12 x, x, = e 11t - 19 X' X2 = 11t 20 19 - 12 19 - 12 3e 11t 20 - 19 20 - 19 2e11t 19 - 12 19 - 12 2e- -11t X2 20 - 19 - 19 20 5e-11t The Wronskian of the solutions is W = Are the solutions linearly independent? O Yes O No The general solution is x(t) = %3D
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 systen. 19 -12 x, x, = e 11t - 19 X' X2 = 11t 20 19 - 12 19 - 12 3e 11t 20 - 19 20 - 19 2e11t 19 - 12 19 - 12 2e- -11t X2 20 - 19 - 19 20 5e-11t The Wronskian of the solutions is W = Are the solutions linearly independent? O Yes O No The general solution is x(t) = %3D
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