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 has an order m $\times$ n, it has mn elements, where m and n are natural numbers.

We have, m $\times$ n = 28

$\Rightarrow$ (m,n) = {(1,28),(2,14),(4,7),(7,4),(14,2),(28,1)}

So, the possible orders are 1 $\times$ 28, 2 $\times$ 14,4 $\times$ 7,7$\times$ 4,14 $\times$ 2,28 $\times$ 1.

Also, if it has 13 elements, then m $\times$ n =13

$\Rightarrow$ (m,n) = {(1,13).(13,1)}

Hence, the possible orders are 1$\times$ 13, 13$\times$1.