# Assume X, Y, Z, W and P are matrices of order, and respectively.

Question:

Assume $X, Y, Z, W$ and $P$ are matrices of order $2 \times n, 3 \times k, 2 \times p, n \times 3$, and $p \times k$ respectively. If $n=p$, then the order of the matrix $7 X-5 Z$ is

$\mathbf{A} p \times 2 \mathbf{B} 2 \times n \mathbf{C} n \times 3 \mathbf{D} p \times n$

Solution:

Matrix X is of the order 2 × n.

Therefore, matrix 7X is also of the same order.

Matrix Z is of the order 2 × p, i.e., 2 × n [Since n = p]

Therefore, matrix 5Z is also of the same order.

Now, both the matrices 7X and 5Z are of the order 2 × n.

Thus, matrix 7X − 5Z is well-defined and is of the order 2 × n.