Let X be the matrix function cos(3 t) sin(3 ) X(t) sin(3 t cos(3 t) Determine if X is a fundamental matrix for system x ' = Ax with 0 A= 3 -3 0 If so, find the solution of the system that satisfies 3 x(0) -5 sin(3t) cos(3t) = 5 3 a) sin(3t) -cos(3) sin(3 ) cos(3t) b) sin(3 t) cos(31) sin(3t) cos(3t) 3 sin(3 t) -cos(3) Not a fundamental solution set d) sin(3 t) cos(3 t) 5 sin(3 t) -cos(3 t) None of the above f)
Let X be the matrix function cos(3 t) sin(3 ) X(t) sin(3 t cos(3 t) Determine if X is a fundamental matrix for system x ' = Ax with 0 A= 3 -3 0 If so, find the solution of the system that satisfies 3 x(0) -5 sin(3t) cos(3t) = 5 3 a) sin(3t) -cos(3) sin(3 ) cos(3t) b) sin(3 t) cos(31) sin(3t) cos(3t) 3 sin(3 t) -cos(3) Not a fundamental solution set d) sin(3 t) cos(3 t) 5 sin(3 t) -cos(3 t) None of the above f)
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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Transcribed Image Text:Let X be the matrix function
cos(3 t)
sin(3 )
X(t)
sin(3 t
cos(3 t)
Determine if X is a fundamental matrix for system x ' = Ax with
0
A=
3
-3
0
If so, find the solution of the system that satisfies
3
x(0)
-5
sin(3t)
cos(3t)
= 5
3
a)
sin(3t)
-cos(3)
sin(3 )
cos(3t)
b)
sin(3 t)
cos(31)
sin(3t)
cos(3t)
3
sin(3 t)
-cos(3)
Not a fundamental solution set
d)
sin(3 t)
cos(3 t)
5
sin(3 t)
-cos(3 t)
None of the above
f)
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