Question

Construct a 3 × 3 matrix whose elements are given by a_ij = `("i" + "j")^3/3`

Answer 1

a₁₁ = `(1 + 1)^3/3 = 2^3/3 = 8/3`

a₁₂ = `(1 + 2)^3/3 = 27/3` = 9

a₁₃ = `(1 + 3)^3/3 = 64/3 = 64/3`

a₂₁ = `(2 + 1)^3/3 = 27/3` = 9

a₂₂ = `(2 + 2)^3/3 = 64/3 = 64/3`

a₂₃ = `(2 + 3)^3/3 = 125/3 = 125/3`

a₃₁ = `(3 + 1)^3/3 = 64/3 = 64/3`

a₃₂ = `(3 + 2)^3/3 = 125/3 = 125/3`

a₃₃ = `(3 + 3)^3/3 = 216/3` = 72

The required matrix A = `[(8/3, 9, 64/3),(9, 64/3, 125/3),(64/3, 125/3, 72)]`