Reword Definition 3.17 for an additive group G . Definition 3.17 : Let G be a group. For any a ∈ G , the subgroup H = { x ∈ G | x = a n f o r n ∈ ℤ } is the subgroup generated by a and is denoted by 〈 a 〉 . The element a is called a generator of H . A given subgroup K of G is a cyclic subgroup if there exists an element b in G such that K = 〈 b 〉 = { y ∈ G | y = b n f o r s o m e n ∈ ℤ } . In particular, G is a cyclic group if there is an element a ∈ G such that G = 〈 a 〉 .
Reword Definition 3.17 for an additive group G . Definition 3.17 : Let G be a group. For any a ∈ G , the subgroup H = { x ∈ G | x = a n f o r n ∈ ℤ } is the subgroup generated by a and is denoted by 〈 a 〉 . The element a is called a generator of H . A given subgroup K of G is a cyclic subgroup if there exists an element b in G such that K = 〈 b 〉 = { y ∈ G | y = b n f o r s o m e n ∈ ℤ } . In particular, G is a cyclic group if there is an element a ∈ G such that G = 〈 a 〉 .
Solution Summary: The author explains the reword of the definition "Let G be a group." The subgroup H=leftxin
Definition
3.17
: Let
G
be a group. For any
a
∈
G
, the subgroup
H
=
{
x
∈
G
|
x
=
a
n
f
o
r
n
∈
ℤ
}
is the subgroup generated by
a
and is denoted by
〈
a
〉
. The element
a
is called a generator of
H
. A given subgroup
K
of
G
is a cyclic subgroup if there exists an element
b
in
G
such that
K
=
〈
b
〉
=
{
y
∈
G
|
y
=
b
n
f
o
r
s
o
m
e
n
∈
ℤ
}
.
In particular,
G
is a cyclic group if there is an element
a
∈
G
such that
G
=
〈
a
〉
.
A research study in the year 2009 found that there were 2760 coyotes
in a given region. The coyote population declined at a rate of 5.8%
each year.
How many fewer coyotes were there in 2024 than in 2015?
Explain in at least one sentence how you solved the problem. Show
your work. Round your answer to the nearest whole number.
Answer the following questions related to the following matrix
A =
3
³).
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