Question

Construct a 3 × 2 matrix whose elements are given by a_ij = e^i.x sinjx.

Answer 1

Let A = `[("a"_11, "a"_12),("a"_21, "a"_22),("a"_31, "a"_32)]_(3 xx 2)`

Given that a_ij = e^i.x sinjx

a₁₁ = e^x sin x

a₁₂ = e^x sin 2x

a₂₁ = e^2x sin x

a₂₂ = e^2x sin 2x

a₃₁ = e^3x sin x

a₃₂ = e^3x sin 2x

Hence, the matrix A = `[("e"^x sin x, "e"^xsin 2x),("e"^(2x) sin x, "e"^(2x) sin 2x),("e"^(3x) ssin x, "e"^(3x) sin 2x)]`