If a matrix has 8 elements, then which of the following will not be a possible order of the matrix?

Options

A. `1xx8`
B. `2xx4`
C. `4xx2`
D. `4xx4`

Answer

To determine which of the given options cannot represent a matrix with 8 elements, we need to understand the relationship between the number of rows (m), the number of columns (n), and the total number of elements in a matrix. The total number of elements in a matrix is given by the product of the number of rows and the number of columns, denoted as \( mn \).

### Step-by-Step Solution:

1. **Understanding the Matrix Order**:
A matrix is defined by its order \( m \times n \), where \( m \) is the number of rows and \( n \) is the number of columns. The total number of elements in the matrix is given by the formula:
\[ \text{Total Elements} = m \times n \]

2. **Given Information**:
We know that the matrix has 8 elements. Therefore, we can set up the equation:
\[ m \times n = 8 \]

3. **Evaluating Each Option**:
- **Option A: \( 1 \times 8 \)**
\[ 1 \times 8 = 8 \quad \text{(Possible)} \]
- **Option B: \( 2 \times 4 \)**
\[ 2 \times 4 = 8 \quad \text{(Possible)} \]
- **Option C: \( 4 \times 2 \)**
\[ 4 \times 2 = 8 \quad \text{(Possible)} \]
- **Option D: \( 4 \times 4 \)**
\[ 4 \times 4 = 16 \quad \text{(Not Possible)} \]

4. **Conclusion**:
The only option that does not yield a product of 8 is option D, \( 4 \times 4 \), which equals 16. Therefore, the answer is that option D is not a possible order for a matrix with 8 elements.

### Final Answer:
The order that will not be a possible order of the matrix is **\( 4 \times 4 \)**.

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