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 2 t [ 1 − 2 ] , x 2 = e 2 t [ − 2 4 ]
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 2 t [ 1 − 2 ] , x 2 = e 2 t [ − 2 4 ]
Solution Summary: The author explains that the vector forms a fundamental solution set or not. 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
2
t
[
1
−
2
]
,
x
2
=
e
2
t
[
−
2
4
]
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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