Question

Construct a 2 x 2 matrix whose elements a_ij are given by `((i + 2j)^2)/(2)`.

Construct a 2 × 2 matrix whose elements in the ith row and jth column are given by:

a_ij = `((i + 2j)^2)/2`

Answer 1

We have a_ij = `((i + 2j)^2)/(2)`

a₁₁ = `((1 + 2 xx 1)^2)/(2) = (9)/(2)`

a₁₂ = `((1 + 2 xx 1)^2)/(2) = (25)/(2)`

a₂₁ = `((2 + 2 xx 1)^2)/(2) = (16)/(2)` = 8

a₂₂ = `((2 + 2 xx 2)^2)/(2)` = 18.

The required matrix

A = `[(a_11 , a_12),(a_21 ,a_22)]`

A = `[(9/2, 25/2),(8,18)]`.