PROBLEM 3 Give the matrix representation for the relation depicted in the arrow dia- gram. Then, express the relation as a set of ordered pairs. The arrow diagram below represents a relation. 2 3 Figure 1: An arrow diagram shows three vertices, 1, 2, and 3. An arrow from verter i points to verter 3, and another errowr from verter 2 points to verter 3. Two self loops are formed, one at verter 1 and another at vertez 2.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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## Problem 3

### Task:
Give the matrix representation for the relation depicted in the arrow diagram. Then, express the relation as a set of ordered pairs.

### Diagram Description:
The arrow diagram below represents a relation.

**Figure 1**: An arrow diagram shows three vertices: 1, 2, and 3. 
- An arrow from vertex 1 points to vertex 3.
- Another arrow from vertex 2 points to vertex 3.
- Two self loops are formed, one at vertex 1 and another at vertex 2.

### Instructions:
1. **Matrix Representation**: Create a matrix reflecting the given arrow diagram.
2. **Set of Ordered Pairs**: Express the relation in terms of ordered pairs based on the diagram.

### Additional Exercise:
Draw the arrow diagram for the relation.

**Domain**: The domain for the relation \( A \) is the set \(\{2, 5, 7, 8, 11\}\). For \( x, y \) in the domain, \( xAy \) if \(|x - y|\) is less than 2.
Transcribed Image Text:## Problem 3 ### Task: Give the matrix representation for the relation depicted in the arrow diagram. Then, express the relation as a set of ordered pairs. ### Diagram Description: The arrow diagram below represents a relation. **Figure 1**: An arrow diagram shows three vertices: 1, 2, and 3. - An arrow from vertex 1 points to vertex 3. - Another arrow from vertex 2 points to vertex 3. - Two self loops are formed, one at vertex 1 and another at vertex 2. ### Instructions: 1. **Matrix Representation**: Create a matrix reflecting the given arrow diagram. 2. **Set of Ordered Pairs**: Express the relation in terms of ordered pairs based on the diagram. ### Additional Exercise: Draw the arrow diagram for the relation. **Domain**: The domain for the relation \( A \) is the set \(\{2, 5, 7, 8, 11\}\). For \( x, y \) in the domain, \( xAy \) if \(|x - y|\) is less than 2.
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Given: The arrow diagram given below:

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