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Q)

If a matrix has 24 elements,what are the possible orders it can have? What, if it has 13 elements?

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A)
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• If a matrix is of order $m\times n.$
• So the element of the matrix is $m\times n.$
• So we have to find all possible order of a matrix with 24 elements.
$\Rightarrow$ Find all ordered pair of natural numbers whose product 24.

$\Rightarrow$ All possible ordered pairs are (1,24),(24,1),(12,2),(2,12),(8,3),(3,8),(6,4),(4,6).

Hence the possible orders are $1\times 24,2\times12,12\times 2,8\times 3,3 \times 8,6\times 4,4\times 6.$

If it has 13 elements the possible order are $1\times13,13\times 1.$

In the above case two types of matrices are formed

(i)Row matrix:

a matrix is said to be row of it has only one row.

$B=[b_{ij}]_{1\times n}$ is a row matrix of order $1\times n.$

$\Rightarrow 1\times 13\rightarrow$ The order is $1\times 13.$

(ii)Column matrix:

A matrix is said to be a column matrix if it has only one column.

A=$[a_{ij}]{m\times 1}$ is a column of matrix of order $m\times 1.$

$\Rightarrow$ The order is $13\times 1$