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Questions  >>  CBSE XII  >>  Math  >>  Matrices

If a matrix has 24 elements,what are the possible orders it can have? (Note: This question has been split into 2 questions)

$\begin{array}{1 1} 1\times24, 24\times1, 2\times12, 12\times2, 3\times 8, 8\times 2, 4\times6\: and\: 6\times4 \\ 1\times 24, 24\times1, 2\times12, 12\times2, 3\times8, 8\times2, \:and\:4\times6 \\ 1\times24, 24\times1, 12\times2, 3\times8, 8\times2, 4\times6\: and\: 6\times4 \\2\times12, 12\times2, 3\times8, 8\times2, 4\times 6\: and\: 6\times4 \end{array} $

1 Answer

  • If a matrix is of order m×n, the number of elements of the matrix is the product m×n. To find the possible orders we have to find all ordered pair of natural numbers whose product is mxn
Given that A matrix contains 24 elements.
$24$ can be expressed as the product of two integers in following ways
$ 1\times 24, 24\times1, 2\times 12, 12\times 2, 3\times8, 8\times3, 4\times 6$ and $6\times4.$
$\therefore$ matrix $A$ can have any of the following orders
$ 1\times 24, 24\times1, 2\times 12, 12\times 2, 3\times8, 8\times3, 4\times 6$ and $6\times4.$
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