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Question
Construct a 3 × 2 matrix whose elements are given by aij = ei.x sinjx.
Solution
Let A = `[("a"_11, "a"_12),("a"_21, "a"_22),("a"_31, "a"_32)]_(3 xx 2)`
Given that aij = ei.x sinjx
a11 = ex sin x
a12 = ex sin 2x
a21 = e2x sin x
a22 = e2x sin 2x
a31 = e3x sin x
a32 = e3x 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)]`
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