In Problems 21-24 , the given vector functions are solutions to a system x ′ ( t ) = A x ( t ) . Determine whether they form a fundamental solution set. If they do, find a fundamental matrix for the system and give a general solution. x 1 = [ e t e t e t ] , x 2 = [ sin t cos t − sin t ] , x 3 = [ − cos t sin t cos t ]
In Problems 21-24 , the given vector functions are solutions to a system x ′ ( t ) = A x ( t ) . Determine whether they form a fundamental solution set. If they do, find a fundamental matrix for the system and give a general solution. x 1 = [ e t e t e t ] , x 2 = [ sin t cos t − sin t ] , x 3 = [ − cos t sin t cos t ]
Solution Summary: The author explains that the given vector forms a fundamental solution set. If they do, find the fundamental matrix and general solution.
In Problems 21-24, the given vector functions are solutions to a system
x
′
(
t
)
=
A
x
(
t
)
. Determine whether they form a fundamental solution set. If they do, find a fundamental matrix for the system and give a general solution.
x
1
=
[
e
t
e
t
e
t
]
,
x
2
=
[
sin
t
cos
t
−
sin
t
]
,
x
3
=
[
−
cos
t
sin
t
cos
t
]
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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