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Questions  >>  CBSE XII  >>  Math  >>  Matrices

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

1 Answer

  • $\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=$5\times 1.$


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