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3 and 4 .Determinants and Matrices
medium
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
A
$p \times 2$
B
$p \times n$
C
$n \times 3$
D
$2 \times n$
Solution
Matrix $X$ is of the order $2 \times n$.
Therefore, matrix $7 X$ is also of the same order.
Matrix $Z$ is of the order $2 \times p,$ i.e, $2 \times n \quad[\text { since } n=p]$
Therefore, matrix $5 Z$ is also of the same order.
Now, both the matrices $7 X$ and $5 Z$ are of the order $2 \times n$.
Thus, matrix $7 X-5 Z$ is well-defined and is of the order $2 \times n$.
Standard 12
Mathematics
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