Determine whether the matrix X(t) given below is a Fundamental Matrix solution of à = Ax, for some A; if yes, find the matrix A. Hint: Yes - means that the Wronskian is not equal to zero. -5 cos 2t -5 sin 2t 3e²t X(t) = -2(cos 2t+ sin 2t) 2(cos 2t - sin 2t) 0 cos 2t sin 2t e2t

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Determine whether the matrix X(t) given below is a Fundamental Matrix solution of
* = Ax, for some A; if yes, find the matrix A. Hint: Yes - means that the Wronskian is
not equal to zero.
- 5 cos 2t
-5 sin 2t
X(t) =
-2(cos 2t + sin 2t) 2(cos 2t - sin 2t)
cos 2t
sin 2t
3e²t
0
e2t
Transcribed Image Text:Determine whether the matrix X(t) given below is a Fundamental Matrix solution of * = Ax, for some A; if yes, find the matrix A. Hint: Yes - means that the Wronskian is not equal to zero. - 5 cos 2t -5 sin 2t X(t) = -2(cos 2t + sin 2t) 2(cos 2t - sin 2t) cos 2t sin 2t 3e²t 0 e2t
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