question_answer 1)

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

Answer:

To find all possible orders of a matrix with 18 elements, we will find all ordered pairs of natural numbers, whose product is 18. Such ordered pairs are (1, 18), (2, 9), (3, 6), (6, 3), (9, 2), (18, 1). Hence possible orders are 1 × 18, 2 × 9, 3 × 6, 6 × 3, 9 × 2, 18 × 1. For a matrix with 5 elements, possible ordered pairs are (1, 5), (5, 1). ? Possible orders are 1 × 5 and 5 ×1.