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

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

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In mathematics, a matrix is a rectangular array which includes numbers, expressions, symbols and equations which are placed in an arrangement of rows and columns. The number of rows and columns that are arranged in the matrix is called as the order or dimension of the matrix. By rule, the rows are listed first and then the columns. 

It is given that the matrix has 28 elements. 

So, according to the rule of matrix,

If the given matrix has mn elements then the dimension of the order can be given by m$\ast$ n, where m and n are natural numbers. 

So, if a matrix has 28 elements which is mn=28, then the following possible orders can be found:

\because \ mn = 28

Take m and n to be any number, so that, when they are multiplied, we get 28.

So, let m = 1 and n = 28.

Then, m \times n = 1 \times 28 ( \ =28)

\Rightarrow 1 \times 28 is a possible order of the matrix with 28 elements

Take m = 2 and n = 14.

Then, m \times n = 2 \times 14 ( \ =28)

\Rightarrow 2 \times 14 is a possible order of the matrix with 28 elements.

Take m = 4 and n = 7.

Then, m \times n = 4 \times 7 ( \ =28)

\Rightarrow 4 \times 7 is a possible order of the matrix with 28 elements.

Take m = 7 and n = 4.

Then, m \times n = 7 \times 4 ( \ =28)

\Rightarrow 7 \times 4 is a possible order of the matrix with 28 elements.

Take m = 14 and n = 2.

Then, m \times n = 14 \times 2 ( \ =28)

\Rightarrow 14 \times 2 is a possible order of the matrix having 28 elements.

Take m = 28 and n = 1.

Then, m \times n = 28 \times 1 ( \ =28)

\Rightarrow 28 \times 1 is a possible order of the matrix with 28 elements.

The following are the possible orders that a matrix having 28 elements can have:

1 \times 28, 2 \times 14, 4 \times 7, 7 \times 4, 14 \times 2 and 28 \times 1

If the given matrix consisted of 13 elements then its possible order can be found out in a similar way as given above:

Here, mn = 13.

Take m and n to be any number so that when multiplied we get 13

Take m = 1 and n = 13.

Then, m \times n = 1 \times \ 13 (=13)

\Rightarrow 1 \times \ 13 is a possible order of the matrix with 13 elements.

Take m = 13 and n = 1.

Then, m \times n = 13 \times 1 ( \ =13)

\Rightarrow 13 \times \ 1 is a possible order of the matrix with 13 elements.

Thus, the possible orders of the matrix consisting of 13 elements are as follows:

1 \times 13 \ and \ 13 \ \times 1

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