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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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• If a matrix is of order $m\times n$.It has mn elements.
• Thus to find all possible orders of a matrix with 18 elements.We will find all ordered pairs of natural numbers whose product is 8.
Thus all possible pairs of 18 are : $18=(1\times 18)(18\times 1)(2\times 9)(9\times 2)(6\times 3)(3\times 6)$
There are 6 matrices of order: $1\times 18,18\times 1,2\times 9,9\times 2,3\times 6,6\times 3$
If 5 elements: 5=$1\times 5$
There are two matrices with 5 elements: $1\times 5,5\times 1$.
Two matrices exists:
Column matrix $\rightarrow$A matrix is said to be a column matrix, if it has only one column.
$m\times 1=5\times 1$
Row matrix $\rightarrow$ A matrix is said to be a row matrix, if it has only one row.
$1\times n=1\times 5$

answered Apr 2, 2013

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