Question

If a matrix has 5 elements, what are the possible orders it can have?

Answer 1

Hint: This question is based on the chapter matrices and determinants. It involves basic concepts like the formation of a matrix using certain rows and columns and also the number of elements it contains.

Complete step-by-step answer:
Now, let us start the question with the assumption of having a certain number of rows and columns.
Let the number of rows be m, and the number of columns is n.
Where m and n are both integers.
Now, the condition given in the question is
\[ \Rightarrow m \times n = 5\]
Let us start assigning some values to the number of rows and find the corresponding column.
If the number of columns comes out to be a positive integer, then the matrix assumed can exist; otherwise, it cannot.
Now, let us start with m = 1; thus, we get,
\[ \Rightarrow 1 \times n = 5\]
After solving for n, we get its value as shown below,
\[ \Rightarrow n = 5\]
As is a positive integer, therefore, the matrix exists.
Now, let us start with m = 2; thus, we get,
\[ \Rightarrow 2 \times n = 5\]
After solving for n, we get its value as shown below,
\[ \Rightarrow n = 2.5\]
As it is not a positive integer, therefore, the matrix does not exist.
Now, let us start with m = 3; thus, we get,
\[ \Rightarrow 3 \times n = 5\]
After solving for n, we get its value as shown below,
\[ \Rightarrow n = 1.67\]
As it is not a positive integer, therefore, the matrix does not exist.
Now, let us start with m = 4; thus, we get,
\[ \Rightarrow 4 \times n = 5\]
After solving for n, we get its value as shown below,
\[ \Rightarrow n = 1.25\]
As it is not a positive integer, therefore, the matrix does not exist.
Now, let us start with m = 5; thus, we get,
\[ \Rightarrow 5 \times n = 5\]
After solving for n, we get its value as shown below,
\[ \Rightarrow n = 1\]
As is a positive integer, therefore, the matrix exists.
Thus, the possible number of the matrix is two.
So, the correct answer is “2”.

Note: This is a question directly from matrices and determinants. One should be well versed with its concepts to solve this question. Do not commit calculation mistakes, and be sure of the final answer.