Question

Construct a 2 × 2 matrix, A = [a_ij], whose elements are given by:

`a_(ij) = i/j`

Answer 1

In general, a 2 × 2 matrix is given by A = `[(a_(11), a_(12)),(a_(21),a_22)]`

`a_(ij) = i/j, i, j = 1, 2`

∴ `a_(11) = 1/1 = 1` 

`a_(12) = 1/2`

`a_(21) = 2/1 = 2`

`a_(22) = 2/2 = 1`

Therefore, the required matrix is A = `[(1, 1/2), (2,1)]`.