Question

If a matrix has $24$ elements, what are the possible it can have? What if it has $13$ elements?

Answer 1

We have to find the number of possible ways a matrix can be formed if it has $24$ and $13$ elements respectively. In order to find that, we have to find the factors of $24$ and $13$ and then the number of products of factors formed would be our required answer.

Complete step by step answer:
Now let us learn about the matrices. A matrix is a grid used to store and display the data in a structured manner. Generally, it is made up of rows and columns. The rows and columns can be as per requirement to display the data. Matrix operations such as addition, subtraction , multiplication , squaring of a matrix etc can be performed upon the matrices. But while performing the multiplication, the row and the respective column of two matrices are to be done respectively.
Now let us find the number of possible ways to represent a matrix if the number of total elements would be $24$ and $13$.
Firstly, we will be finding the factors of $24$. We get,

& 1\times 24=24 \\\ & 2\times 12=24 \\\ & 3\times 8=24 \\\ & 4\times 6=24 \\\ & 6\times 4=24 \\\ & 8\times 3=24 \\\ & 12\times 2=24 \\\ & 24\times 1=24 \\\ \end{aligned}$$ $$\therefore $$ The possible orders of a matrix with $$24$$ elements are $$1\times 24,2\times 12,3\times 8,4\times 6,6\times 4,8\times 3,12\times 2,24\times 1$$. Now let's check the case if the matrix has $$13$$ elements. Let us find out the factors first. We get, $$\begin{aligned} & 1\times 13=13 \\\ & 13\times 1=13 \\\ \end{aligned}$$ **$$\therefore $$ The possible orders of a matrix with $$13$$ elements are $$1\times 13,13\times 1$$.** **Note:** We must be careful while representing the elements in a matrix, as it should be properly arranged for accurate answers or else this could give an incorrect answer. We can use matrices in various fields such as time-sensitive engineering applications and many more. Multiplication of matrices could be complicated, so we must be careful while performing multiplication upon matrices.