In Problem 29-30 , verify that X ( t ) is a fundamental matrix for the given system and compute X − 1 ( t ) . Use the result of Problem 28 to find the solution to the initial value problem. x ′ = [ 0 6 0 1 0 1 1 1 0 ] x , x ( 0 ) = [ − 1 0 1 ] X ( t ) = [ 6 e − t − 3 e − 2 t 2 e 3 t − e − t e − 2 t e 3 t − 5 e − t e − 2 t e 3 t ]
In Problem 29-30 , verify that X ( t ) is a fundamental matrix for the given system and compute X − 1 ( t ) . Use the result of Problem 28 to find the solution to the initial value problem. x ′ = [ 0 6 0 1 0 1 1 1 0 ] x , x ( 0 ) = [ − 1 0 1 ] X ( t ) = [ 6 e − t − 3 e − 2 t 2 e 3 t − e − t e − 2 t e 3 t − 5 e − t e − 2 t e 3 t ]
Solution Summary: The author explains that the X(t) is a fundamental matrix for the given system.
In Problem 29-30, verify that
X
(
t
)
is a fundamental matrix for the given system and compute
X
−
1
(
t
)
. Use the result of Problem 28 to find the solution to the initial value problem.
x
′
=
[
0
6
0
1
0
1
1
1
0
]
x
,
x
(
0
)
=
[
−
1
0
1
]
X
(
t
)
=
[
6
e
−
t
−
3
e
−
2
t
2
e
3
t
−
e
−
t
e
−
2
t
e
3
t
−
5
e
−
t
e
−
2
t
e
3
t
]
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