Question

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

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

∴ `a_11 = (1 + 2)^2/(2) = (3^2)/2 = 9/2`

`a_12 = (1 + 4)^2/2 = 5^2/2 = (25)/(2)`

`a_21 = (2 + 2^2)/(2) = (4^2)/(2) = 8`

`a_22 = (2 + 4)^2/(2) = (6^2)/2 = 18`

Therefore, the required matrix is A = `[(9/2, 25/2),(8,18)]`.