If a matrix contains 20 elements , then the order of the matrix can be _______.

Options

A. `5xx4`
B. `20xx1`
C. `1xx20`
D. All the above

Answer

To determine the order of a matrix that contains 20 elements, we need to understand the relationship between the number of rows (R) and the number of columns (C) in a matrix. The order of a matrix is typically represented as R x C, where R is the number of rows and C is the number of columns.

### Step-by-Step Solution:

1. **Understand the Concept**: The total number of elements in a matrix can be calculated using the formula:
\[ \text{Number of elements} = R \times C \]
where R is the number of rows and C is the number of columns.

2. **Set Up the Equation**: Given that the matrix contains 20 elements, we can set up the equation:
\[ R \times C = 20 \]

3. **Find the Factors of 20**: To find possible values for R and C, we need to determine the factors of 20. The factors of 20 are:
- 1 and 20
- 2 and 10
- 4 and 5
- 5 and 4
- 10 and 2
- 20 and 1

4. **List Possible Orders**: From the factors, we can derive the possible orders of the matrix:
- \(1 \times 20\)
- \(2 \times 10\)
- \(4 \times 5\)
- \(5 \times 4\)
- \(10 \times 2\)
- \(20 \times 1\)

5. **Conclusion**: Therefore, the possible orders of the matrix that contains 20 elements can be:
- \(1 \times 20\)
- \(2 \times 10\)
- \(4 \times 5\)
- \(5 \times 4\)
- \(10 \times 2\)
- \(20 \times 1\)

### Final Answer:
The order of the matrix can be \(1 \times 20\), \(2 \times 10\), \(4 \times 5\), \(5 \times 4\), \(10 \times 2\), or \(20 \times 1\).

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