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Leviafan [203]
3 years ago
5

I WILL GIVE BRAINY LIST    PLEASE HELP

Mathematics
1 answer:
kotegsom [21]3 years ago
3 0
It is twice the area of a square of side lengths 3 units
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Determine,in each of the following cases, whether the described system is or not a group. Explain your answers. Determine what i
zheka24 [161]

Answer:

(a) Not a group

(b) Not a group

(c) Abelian group

Step-by-step explanation:

<em>In order for a system <G,*> to be a group, the following must be satisfied </em>

<em> (1) The binary operation is associative, i.e., (a*b)*c = a*(b*c) for all a,b,c in G </em>

<em>(2) There is an identity element, i.e., there is an element e such that a*e = e*a = a for all a in G </em>

<em> (3) For each a in G, there is an inverse, i.e, another element a' in G such that a*a' = a'*a = e (the identity) </em>

<em> </em>

If in addition the operation * is commutative (a*b = b*a for every a,b in G), then the group is said to be Abelian

(a)  

The system <G,*> is not a group since there are no identity.  

To see this, suppose there is an element e such that  

a*e = a

then  

a-e = a which implies e=0

It is easy to see that 0 cannot be an identity.

For example  

2*0 = 2-0 = 2

Whereas

0*2 = 0-2 = -2

So 2*0 is not equal to 0*2

(b)

The system <G,*> is not a group either.

If A is a matrix 2x2 and the determinant of A det(A)=0, then the inverse of A does not exist.

(c)

The table of the operation G is showed in the attachment.

It is evident that this system is isomorphic under the identity map, to the cyclic group

\mathbb{Z}_{5}

the system formed by the subset of Z, {0,1,2,3,4} with the operation of addition module 5, which is an Abelian cyclic group

We conclude that the system <G,*> is Abelian.

Attachment: Table for the operation * in (c)

4 0
3 years ago
Mr cho drives 45 miles in 1 hours.if her speed stays constants, how many hours will it take for her to drive 405 miles
-Dominant- [34]
With constant speed it will take her : 405 ml / 45= 9 hours of drive
6 0
2 years ago
What is seventy divided by four?
Nataly_w [17]

Answer:

17.5

Step-by-step explanation:

17×4=68; half of 4 is 2; 68+2=70

5 0
3 years ago
Read 2 more answers
An elevator is on the 20th floor. it goes down 11 floors and then up 5 floors .what floor is the elevator on noW.
amm1812

Answer: 14th floor

Step-by-step explanation:

20 - 11 + 5 = 14

4 0
3 years ago
Read 2 more answers
Someone please help me
exis [7]
V = 1/3 l h w

V = 1/3 (12)(15)(9)
V= = 540

answer 540 m^3
8 0
3 years ago
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