If a matrix has 28 elements, what are the possible orders it can … - Vidyadip

Question

If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?

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Answer

We know that, if a matrix is of order m × n, it has mn elements, where m and n are natural numbers.
We have, m × n = 28
⇒ (m, n) = {(1, 28), (2, 14), (4, 7), (7, 4), (14, 2), (28, 1)}
So, the possible orders are 1 × 28, 2 × 14, 4 × 7, 7 × 4, 14 × 2, 28 × 1
Also, if it has 13 elements, then m × n = 13
(m, n) = {(1, 13), (13, 1)}
Hence, the possible orders are 1 × 13, 13 × 1.

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