Composition of Matrix relation I am unsure if this exercise is possible to do, could anyone tell me

rzfansubs87 2022-07-12 Answered
Composition of Matrix relation
I am unsure if this exercise is possible to do, could anyone tell me if I am correct or not?
We have DOMAIN { 1 , 2 , 3 } and RANGE { 1 , 2 , 3 , 4 } and relation R = { ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) }.
The exercise say to find R 2 .
I have tried two way to find this.
1. Matrix composition. Here i cam across the problem that you cannot compose a 3 × 4 matrix with another 3 × 4.
2. Compose the relations themselves what i get is { ( 1 , 3 ) , ( 2 , 4 ) , ( 3 , ? ) }
I cant see how i can find the 4 to replace ?
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Answers (1)

Jamiya Costa
Answered 2022-07-13 Author has 18 answers
Step 1
Interpretation 2 is correct (interpretation 1 is not). According to the prescription for R,
1 2 ,     2 3 ,     3 4 ..
Then, if we compose R with itself, we get
1 2 3 ,     2 3 4 ,     3 4 (nothing) ..
Step 2
That is, in the last spot, since 4 is not in the domain of R, we can't plug 3 into R 2 . Thus, 3 is not in the domain of R 2 , and the relation R 2 is defined by the prescription
R 2 : 1 3 ,     2 4 .
In the language of ordered pairs, R 2 = { ( 1 , 3 ) , ( 2 , 4 ) } ..
The domain is the set { 1 , 2 }, and the range is the set { 3 , 4 }.

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