Question

Construct a matrix A = [a_ij]_2×2 whose elements a_ij are given by a_ij = e^2ix sin jx.

Answer 1

For i = 1, j = 1, a₁₁ = e^2x sin x

For i = 1, j = 2, a₁₂ = e^2x sin 2x

For i = 2, j = 1, a₂₁ = e^4x sin x

For i = 2, j = 2, a₂₂ = e^4x sin 2x

Thus A = `[("e"^(2x) sin x, "e"^(2x) sin 2x),("e"^(4x) sin x, "e"^(4x) sin 2x)]`