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

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

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 if a matrix is of order m x n, it has mn elements. Therefore, for finding all possible orders of a matrix with 8 elements, we will find all ordered pairs of natural numbers, whose product is 8.

∴ all possible ordered pairs are (1.8), (8, I), (4, 2). (2, 4)
∴ possible orders are I x 8, 8 x 1, 2 x 4, 4 x 2.

Let A = [ a_ii] be required 3 x 4 matrix where a_ij= i + j
a₁₁ = 1 + 1 = 2, a₁₂ =1+2, a₁₃=1 + 3 = 4, a₁₄ = 1 + 4 = 5
      a₂₁ = 1 + 1 = 2, a₂₂ =1+2, a₂₃=1 + 3 = 4, a₂₄ = 1 + 4 = 6
      a₃₁ = 1 + 1 = 2, a₃₂ =1+2, a₃₃=1 + 3 = 4, a₃₄ = 1 + 4 = 7