Question

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

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

`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

∴ A = `[(2, 9/2), (9/2 , 8)]`