Consider the following information regarding the number of men and women workers in three factories I. II and III

	Men Workers	Women Workers
I	30	25
II	25	31
III	27	26

Represent the above information in the form of a 3 x 2 matrix. What does the entry in the third row and second column represent?

The given information is

The information is represented in the form of a 3 X 2 matrix as follows :



The entry in the third row and second column represents the number of women workers in factory III.

          

We know that a matrix of order m x n has mn elements. Therefore, for finding all possible orders of a matrix with 24 elements, w e will find all ordered pairs with products of elements as 24.
∴ all possible ordered pairs are
(1, 24), (24. 1), (2, 12), (12. 2). (3, 8), (8, 3), (4. 6), (6, 4)
∴ possible orders are
1 x 24. 24 x 1, 2 x 12, 12 x 2, 3 x 8, 8 x 3, 4 x 6. 6 x 4
If number of elements  =13, then possible orders are 1 x 13, 13 x l.

Let A = [a i] be required 3 x3 matrix    
where a,ij , = 2 i – 3 j    
∴ a₁₁, = 2–3 = –1. a₁₂ = 2–6 = 4. a₁₃,= 2–9 = 7
a₂₁ = 4 — 3 = 1. a₂₂ = 4 — 6 = —2 . a₂₃  = 4 –9 = 5
a₃₁ = 6 – 3 = 3, = 6 – 6 = 0 , a₃₃ = 6 – 9 = –3

We know that a matrix of order m x n has mnelements. Therefore, for finding all possible orders of a matrix with 18 elements, we will find all ordered pairs with products of elements as 18
∴ all possible ordered pairs areall possible ordered pairs areall possible ordered pairs areall possible ordered pairs areall possible ordered pairs areall possible ordered pairs are
(I, 18). (18, 1). (2, 9). (9. 2). (3, 6). (0, 3)
∴ possible orders are 1 x 18. 18 x 1. 2 x 9,-9 X 2, 3 x 6. 6 x 3.
If number of elements = 5, then possible orders arc 1 x 5. 5 x I.

Number of elements = 12
∴possible orders of the matrix are
1 x 12, 12 x 1,2 X 6. 6 x 2,3 x 4,4 x 3
If numbers of elements = 7, then possible orders are 1 x 7. 7 x 1