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

We know that in mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

The number of rows and columns that a matrix has is called its order or its dimension. By convention, rows are listed first; and columns second.

We are given with a matrix that has 28 elements.

We know that,

If a matrix has mn elements, then the order of the matrix can be given by m × n, where m and n are natural numbers.

Therefore, for a matrix having 28 elements, that is, mn = 28, possible orders can be found out as follows:

∵ mn = 28

Take m and n to be any number, such that, when it is multiplied it gives 28.

So, let m = 1 and n = 28.

Then, m × n = 1 × 28 (=28)

⇒ 1 × 28 is a possible order of the matrix having 28 elements.

Take m = 2 and n = 14.

Then, m × n = 2 × 14 (=28)

⇒ 2 × 14 is a possible order of the matrix having 28 elements.

Take m = 4 and n = 7.

Then, m × n = 4 × 7 (=28)

⇒ 4 × 7 is a possible order of the matrix having 28 elements.

Take m = 7 and n = 4.

Then, m × n = 7 × 4 (=28)

⇒ 7 × 4 is a possible order of the matrix having 28 elements.

Take m = 14 and n = 2.

Then, m × n = 14 × 2 (=28)

⇒ 14 × 2 is a possible order of the matrix having 28 elements.

Take m = 28 and n = 1.

Then, m × n = 28 × 1 (=28)

⇒ 28 × 1 is a possible order of the matrix having 28 elements.

Thus, the possible orders of the matrix having 28 elements are

1 × 28, 2 × 14, 4 × 7, 7 × 4, 14 × 2 and 28 × 1

If the matrix had 13 elements, then also we find the possible order in same way.

Here, mn = 13.

Take m and n to be any number, such that, when it is multiplied it gives 13.

Take m = 1 and n = 13.

Then, m × n = 1 × 13 (=13)

⇒ 1 × 13 is a possible order of the matrix having 13 elements.

Take m = 13 and n = 1.

Then, m × n = 13 × 1 (=13)

⇒ 13 × 1 is a possible order of the matrix having 13 elements.

Thus, the possible orders of the matrix having 13 elements are

1 × 13 and 13 × 1