Problems For Problems 3 − 22 , express S in set notation and determine whether it is a subspace of the given vector space V . V is the vector space of all real valued functions defined on the interval [ a , b ] , and S is the subset of V consisting of all real valued functions [ a , b ] satisfying f ( a ) = 5 ⋅ f ( b ) .
Problems For Problems 3 − 22 , express S in set notation and determine whether it is a subspace of the given vector space V . V is the vector space of all real valued functions defined on the interval [ a , b ] , and S is the subset of V consisting of all real valued functions [ a , b ] satisfying f ( a ) = 5 ⋅ f ( b ) .
Solution Summary: The author explains that if S is a nonempty subspace of the vector space V, it is closed under addition and scalar multiplication.
For Problems
3
−
22
, express
S
in set notation and determine whether it is a subspace of the given vector space
V
.
V
is the vector space of all real valued functions defined on the interval
[
a
,
b
]
, and
S
is the subset of
V
consisting of all real valued functions
[
a
,
b
]
satisfying
f
(
a
)
=
5
⋅
f
(
b
)
.
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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