If a matrix has 24 elements, what are the possible orders it can … - Vidyadip

Question

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

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Answer

We know that a matrix of order m × n has mn elements. Therefore, for finding all possible orders of a matrix with 24 elements, we will find all ordered pairs with products of elements as 24.$\therefore$ all possible ordered pairs are
(1, 24), (24, 1), (2, 12), (12, 2), (3, 8), (8, 3), (4, 6), (6, 4)
$\therefore$ possible orders are
1 × 24, 24 × 1, 2 × 12, 12 × 2, 3 × 8, 8 × 3, 4 × 6, 6 × 4
if number of elements = 13, then possible orders are 1 × 13, 13 × 1.

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