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# If a matrix has 18 elements,what are the possible orders it can have?What, if it has 5 elements?

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• $\Rightarrow$ If it has 18 elements.
• If a matrix is of order $m\times n$.
• Then the elements of the matrix is mn.(i.e product of the order)
• $\Rightarrow$ find all possible orders of a matrix with 18 element.
• $\Rightarrow$ Find all ordered pair of natural number whose product is 18.
• $\Rightarrow$ possible ordered pair are $1\times 18,18\times 1,9\times 2,2\times 9,6\times 3,3\times 6.$
If it has 5 elements.

The orders are $(1\times 5),(5\times 1).$

Two types of matrix formed

(i)Row matrix:

A matrix is said to be a row matrix of order $1\times n.$

$\Rightarrow$ The order of matrix of element 5=$1\times 5.$

$\Rightarrow 1\times n=1\times 5.$

(ii)Column matrix:

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

The order of matrix of element 5=$5\times 1.$