For each divisor k > 1 of n , let U k ( n ) = { x ∈ U ( n ) | x mod k = 1 } .[For example, U 3 ( 21 ) = { 1 , 4 , 10 , 13 , 16 , 19 } and U 7 ( 21 ) = { 1 , 8 } .]List the elements of U 4 ( 20 ) , U 5 ( 20 ) , U 5 ( 30 ) , and U 10 ( 30 ) . Prove that U k ( n ) is a subgroup of U ( n ). Let H = { x ∈ U ( 10 ) | x mod 3 = 1 } . Is H a subgroup of U (10)? (This exercise is referred to in Chapter 8.)
For each divisor k > 1 of n , let U k ( n ) = { x ∈ U ( n ) | x mod k = 1 } .[For example, U 3 ( 21 ) = { 1 , 4 , 10 , 13 , 16 , 19 } and U 7 ( 21 ) = { 1 , 8 } .]List the elements of U 4 ( 20 ) , U 5 ( 20 ) , U 5 ( 30 ) , and U 10 ( 30 ) . Prove that U k ( n ) is a subgroup of U ( n ). Let H = { x ∈ U ( 10 ) | x mod 3 = 1 } . Is H a subgroup of U (10)? (This exercise is referred to in Chapter 8.)
Solution Summary: The author explains that U_k(n) is a subgroup of
For each divisor
k
>
1
of n, let
U
k
(
n
)
=
{
x
∈
U
(
n
)
|
x
mod
k
=
1
}
.[For example,
U
3
(
21
)
=
{
1
,
4
,
10
,
13
,
16
,
19
}
and
U
7
(
21
)
=
{
1
,
8
}
.]List the elements of
U
4
(
20
)
,
U
5
(
20
)
,
U
5
(
30
)
,
and
U
10
(
30
)
. Prove that
U
k
(
n
)
is a subgroup of U(n). Let
H
=
{
x
∈
U
(
10
)
|
x
mod
3
=
1
}
. Is H a subgroup of U(10)? (This exercise is referred to in Chapter 8.)
a)
[1√2-31x+1√3-11y = x (1 - √2) + √34
LI√2-21x-1√3-3/4= √34 -
√2x-4
Please Help me answer this linear algebra question. This is a practice textbook question.
1. a scientist observed a bacterium in a microscope. it measured about .0000029 meter in diameter which of the following is closest to it? A- 2 x 10^-6, B- 2 x 10^-5, C- 3 x 10^-5, or D- 3 x 10^-6
2.express the product of 500 and 400 in scientific notation. is it 2 x 10^5 or 2 x 10^4 or 2 x 10^3 or 20 x 10^4
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