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# 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 $7X - 5Z$ is:

$$(A) \quad p \times 2 \qquad \qquad (B) \quad 2 \times n \qquad \qquad (C) \quad n \times 3 \qquad \qquad (D) \quad p \times n$$

Toolbox:
• Multiplication of two matrices is defined only if the number of columns of the left matrix is the same as the number of rows of the right matrix.
The order of matrix X is $2\times n.$
The order of matrix Z is $2\times p.$
$7X-5Z$ can be defined only $X$ and $Z$ are of the same order, i.e, $n$ must equal $p$.
Thus the order of 7X-5Z is $2\times n$ or $2\times p$
edited Mar 1, 2013