Question

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

a_ij = `(3i - 2j)/2`

Answer 1

We have a_ij = `(3i - 2j)/2`

a₁₁ = `(3(1) - 2(1))/2 = (3 - 2)/2 = 1/2`

a₁₂ = `(3(1) - 2(2))/2 = (3 - 4)/2 = (-1)/2`

a₂₁ = `(3(2) - 2(1))/2 = (6 - 2)/2` = 2

a₂₂ = `(3(2) - 2(2))/2 = (6 - 4)/2 = 1`

∴ The required matrix is `[(1/2, (-1)/2),(2, 1)]`