Given that matrices A and B are of order `3 xx n and m xx 5` respectively, then the order of matrix C = 5A + 3B is:

Options

A. `3xx5 and m=n`
B. `3xx5`
C. `3xx3`
D. `5xx5`

Answer

To find the order of the matrix \( C = 5A + 3B \), we need to analyze the orders of matrices \( A \) and \( B \) given in the problem.

1. **Identify the order of matrix A**:
- Matrix \( A \) is given to be of order \( 3 \times n \). This means it has 3 rows and \( n \) columns.

2. **Identify the order of matrix B**:
- Matrix \( B \) is given to be of order \( m \times 5 \). This means it has \( m \) rows and 5 columns.

3. **Determine the conditions for addition**:
- For the matrices \( 5A \) and \( 3B \) to be added together, they must have the same order. This means the number of rows and columns in both matrices must be equal.

4. **Set the orders equal**:
- The order of \( 5A \) will be the same as the order of \( A \), which is \( 3 \times n \).
- The order of \( 3B \) will be the same as the order of \( B \), which is \( m \times 5 \).
- For \( 5A \) and \( 3B \) to be added, we need:
\[ 3 = m \quad \text{(number of rows)} \]
\[ n = 5 \quad \text{(number of columns)} \]

5. **Substitute values into matrix C**:
- Now that we know \( m = 3 \) and \( n = 5 \), we can find the order of matrix \( C \):
- The order of \( C \) will be the same as the order of \( 5A \) (or \( 3B \)), which is:
\[ C = 5A + 3B \implies \text{Order of } C = 3 \times 5 \]

6. **Final answer**:
- Therefore, the order of matrix \( C \) is \( 3 \times 5 \).

### Summary:
The order of matrix \( C \) is \( 3 \times 5 \).