Question

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

Answer 1

These types of problems are in general simple in nature and are very easy to solve. This question can be solved very quickly once we understand all the core concepts involved in this problem. We need to have a fair amount of idea of chapters and topics like matrices and determinants. A matrix can be of any order, which means a matrix can be a square matrix or it can be a rectangular matrix. A determinant on the other hand is always square. Suppose if a matrix is of order $3\times 4$ , then it means that the matrix has a total of $12$ elements and among them, the matrix consists of $3$ columns and $4$ rows.

Complete step by step answer:
Now we start off with the solution of the given problem by trying to find out the order of a matrix which has $28$ elements in it. To find the order one thing we can clearly say is that, the product of any pair of numbers which results in $28$ can be an order of this matrix. Some of the findings are, $7\times 4,4\times 7,2\times 14,14\times 2,28\times 1,1\times 28$ . All these can be the order of the matrix of $28$ elements. Now if the matrix has $13$ elements in it, the possible orders of the matrices are, $13\times 1$ , which is a column matrix and $1\times 13$ which is a row matrix.

Note: Problems of these types require some previous background knowledge of matrices and determinants and their various properties. While we find the pair of numbers or the order we need to make sure that, the matrix can accommodate all the given number of elements. In case of the order of any given matrix $n\times 1,1\times n$ are always possible, where ‘n’ is the number of elements in the matrix.