If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
The order of the matrix is defined as m × n , whose product is given as m n . To find all the possible orders of a matrix having 18 elements, we have to find the all the ordered pairs of natural numbers which gives the product of 18 .
The ordered pairs of rows and columns to get 18 elements are: ( 1 , 18 ) , ( 18 , 1 ) , ( 2 , 9 ) , ( 9 , 2 ) , ( 3 , 6 ) and ( 6 , 3 ) .
Hence, the possible orders of a matrix having 18 elements are 1 × 18 , 18 × 1 , 2 × 9 , 9 × 2 , 3 × 6 and 6 × 3 .
If the matrix has 5 elements, the possible ordered pairs of natural numbers are: ( 1 , 5 ) and ( 5 , 1 ) .
Thus, the possible order of a matrix having 5 elements are 1 × 5 and 5 × 1 .
The order of the matrix is defined as
The ordered pairs of rows and columns to get 18 elements are:
Hence, the possible orders of a matrix having
If the matrix has
Thus, the possible order of a matrix having 5 elements are
