Question

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

`a_(ij) = (i + j)^2/2`

Answer 1

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

`a_ij = (i + j)^2/2; i, j = 1, 2`

∴ `a_(11) = (1 + 1)^2/2 = 4/2 = 2` 

`a_(12) = (1 + 2)^2/2 = 9/2`

`a_(21) = (2 + 1)^2/2 = 9/2`

`a_(22) = (2 + 2)^2/2= 16/2 = 8`

Therefore, the required matrix is A = `[(2, 9/2), (9/2, 8)]`.