Question

Construct a_{2 × 2} matrix where a_ij = `("i" - 2"j")^2/2`

Answer 1

Let A = `[("a"_11, "a"_12),("a"_21, "a"_22)]_(2 xx 2)`

Given that a_ij = `("i" - 2"j")^2/2`

a₁₁ = `(1 - 2 xx 1)^2/2 = 1/2`

a₁₂ = `(1 - 2 xx 2)^2/2 = 9/2`

a₂₁ = `(2 - 2 xx 1)^2/2` = 0

a₂₂ = `(2 - 2 xx 2)^2/2` = 2

Hence, the matrix A = `[(1/2, 9/2),(0, 2)]`