Question

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

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

Answer 1

A 2 × 2 matrix has 2 rows and 2 columns.

So, it is given by

A = `[a_(ij)]_(2 × 2) = [(a_(11), a_(12)),(a_(21),a_22)]`

For `a_(ij) = (1 + 2j)^2/2`, we have

`a_11 = ((1 + 2 xx 1)^2)/(2) = (9)/(2)`

`a_12 = ((1 + 2 xx 1)^2)/(2) = (25)/(2)`

`a_21 = ((2 + 2 xx 1)^2)/(2) = (16)/(2)` = 8

`a_22 = ((2 + 2 xx 2)^2)/(2) = 36/2` = 18

∴ A = `[(9/2, 25/2),(8,18)]`