Question

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A matrix has 18 elements. What are the possible orders it can have ? What if it has 5 elements.

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Answer 1

The possible orders a matrix with 18 elements can have are; (1, 18), (2, 9), (3, 6), (6, 3), (9, 2), and (18, 1).

The possible orders a matrix with 5 elements can have are; (1, 5) and (5, 1).

Step-by-step explanation:

We are given that a matrix has 18 elements. And we have to find the possible orders it can have.

Firstly, as we know if a matrix is of the order $m \times n$, then it must have $mn$ elements; where m is the number of rows and n is the number of columns in a matrix.

Now, if there are 18 elements in a matrix, then we have to find the pair of numbers whose product is equal to 18, i.e;

Number of rows $\times$ Number of columns = 18

1 $\times$ 18 = 18

2 $\times$ 9 = 18

3 $\times$ 6 = 18

6 $\times$ 3 = 18

9 $\times$ 2 = 18

18 $\times$ 1 = 18

Hence, the possible orders a matrix with 18 elements can have are; (1, 18), (2, 9), (3, 6), (6, 3), (9, 2), and (18, 1).

Similarly, if a matrix has 5 elements, then the pair of numbers whose product is equal to 5 are;

1 $\times$ 5 = 5

5 $\times$ 1 = 5

Hence, the possible orders a matrix with 5 elements can have are; (1, 5) and (5, 1).

Answer 2

A matrix consisting of 18 elements will be presented in the following order:

1  ×  18  =  18

2  ×   9   =  18

3  ×   6   =  18

6  ×   3   =  18

9  ×   2   =  18

18  ×   1   =  18

so,

Number of rows × Number of columns = 18

∴ The possible orders here can be,

(1 × 18), (2 × 9), (3 × 6), (6 × 3), (9 × 2), (18 × 1)

However, if a matrix has 5 elements, it will be ordered as follows:

1   ×  5   =  5 5  ×   1  =   5

∴ The possible orders here are,

(1 × 5), (5 × 1)