Question

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

Answer 1

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.