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 [ 3 2 ] , x 2 = e 4 t [ 1 − 1 ]
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 [ 3 2 ] , x 2 = e 4 t [ 1 − 1 ]
Solution Summary: The author explains that the given vector forms a fundamental solution set. The fundamental matrix and general solution is left[cc3e-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
[
3
2
]
,
x
2
=
e
4
t
[
1
−
1
]
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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