Question

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

Answer 1

We know that if a matrix is of the order m × n, it has mn elements. Thus, to find all the possible orders of a matrix having 18 elements, we have to find all the ordered pairs of natural numbers whose product is 18.

The ordered pairs are (1, 18), (18, 1), (2, 9), (9, 2), (3, 6), and (6, 3).

Hence, the possible orders of a matrix that has 18 elements are 1 × 18, 18 × 1, 2 × 9, 9 × 2, 3 × 6 and 6 × 3.

(1, 5) and (5, 1) are the ordered pairs of natural numbers whose product is 5.

Hence, the possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1.