A matrix of order `mxxn` contains 7 elements, then how many different order pairs (m,n) can take ?

Options

A. `2`
B. `1`
C. `3`
D. `7`

Explanation

To solve the problem of finding the different ordered pairs \((m, n)\) for a matrix of order \(m \times n\) that contains 7 elements, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Matrix Elements**:
A matrix of order \(m \times n\) contains \(m \times n\) elements. According to the problem, the total number of elements is 7. Therefore, we can set up the equation:
\[ m \times n = 7 \]

2. **Finding Factor Pairs**:
To find the ordered pairs \((m, n)\), we need to determine the factor pairs of 7. The factors of 7 are 1 and 7 since 7 is a prime number.

3. **Listing the Ordered Pairs**:
The factor pairs of 7 can be expressed as:
- \( (1, 7) \)
- \( (7, 1) \)

4. **Conclusion**:
Thus, the different ordered pairs \((m, n)\) that satisfy the condition \(m \times n = 7\) are:
- \( (1, 7) \)
- \( (7, 1) \)

5. **Counting the Ordered Pairs**:
Therefore, the total number of different ordered pairs \((m, n)\) is 2.

### Final Answer:
The number of different ordered pairs \((m, n)\) is **2**.

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