Assume X,Z are the matrices of order `2 xx n`,`2 xx p` respectively. If `n=p`, then the order of the matrix `7X-5Z`is:(A) `p xx2` (B) `2xx n` (C) `n xx3` (D) `p xxn`

Options

A. `pxx2`
B. `2xxn`
C. `nxx3`
D. `pxxn`

Explanation

To solve the problem, we need to determine the order of the matrix \(7X - 5Z\) given that \(X\) and \(Z\) are matrices of orders \(2 \times n\) and \(2 \times p\) respectively, and that \(n = p\).

### Step-by-Step Solution:

1. **Identify the orders of matrices \(X\) and \(Z\)**:
- The order of matrix \(X\) is given as \(2 \times n\).
- The order of matrix \(Z\) is given as \(2 \times p\).

2. **Since \(n = p\)**:
- We can substitute \(p\) with \(n\). Thus, the order of matrix \(Z\) can also be expressed as \(2 \times n\).

3. **Determine the order of \(7X\)**:
- When we multiply a matrix by a scalar (like 7), the order of the matrix remains unchanged.
- Therefore, the order of \(7X\) is still \(2 \times n\).

4. **Determine the order of \(5Z\)**:
- Similarly, multiplying matrix \(Z\) by 5 does not change its order.
- Thus, the order of \(5Z\) is also \(2 \times n\).

5. **Find the order of the matrix \(7X - 5Z\)**:
- To subtract two matrices, they must have the same order.
- Since both \(7X\) and \(5Z\) have the order \(2 \times n\), the order of the resulting matrix \(7X - 5Z\) will also be \(2 \times n\).

6. **Conclusion**:
- Therefore, the order of the matrix \(7X - 5Z\) is \(2 \times n\).

### Final Answer:
The order of the matrix \(7X - 5Z\) is \(2 \times n\), which corresponds to option (B).

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