Let's break down the two parts of your question and answer them in detail.
### 3. Show the interval notation (-2,3) on the number line.
To show the interval notation (-2,3) on the number line, follow these steps:
1. Identify the Endpoints: The interval (-2, 3) includes all the numbers between -2 and 3 but does not include -2 and 3 themselves. This is indicated by the use of parentheses.
2. Draw the Number Line:
- Draw a horizontal line and mark points on the line at regular intervals.
- Place the points -2 and 3 on the number line.
3. Mark the Interval:
- Because the interval (-2,3) does not include the endpoints -2 and 3, use open circles (◯) at -2 and 3. Open circles indicate that these points are not included in the interval.
- Shade the section of the number line between -2 and 3 to indicate that all the numbers between -2 and 3 are included in the interval.
Here is a visual representation:
```
◯----------------◯
-2 3
```
The shaded part between the open circles represents the interval (-2, 3).
### 4. Define a Singleton Set in Matrix Terms.
A singleton set in matrix terms refers to a set that contains exactly one element. When dealing with a matrix, this would mean a matrix that consists of a single element.
#### Example:
Consider a 1x1 matrix:
```
A = [a]
```
Here, the set of matrices is a singleton because it contains only one element 'a'. This can be thought of as a 1-dimensional matrix with only one entry.
In set notation, a singleton set is often written as:
```
{a}
```
where 'a' is the unique element in the set. In matrix terms, it can be represented by the matrix containing only the element 'a'.
This concludes the detailed steps and explanations for showing the interval (-2,3) on a number line and defining a singleton set in the context of matrices.
