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Question
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = `(("i" + "j")^3)/5`
Solution
A = [aij]3 × 2 = `[("a"_11, "a"_12),("a"_21, "a"_22),("a"_31, "a"_32)]`
Given that aij = `(("i" + "j")^3)/5`
∴ a11 = `((1 + 1)^3)/5 = 2^3/5 = 8/5`
a12 = `((1 + 2)^3)/5 = 3^3/5 = 27/5`
a21 = `((2 + 1)^3)/5 = 3^3/5 = 27/5`
a22 = `((2 + 2)^3)/5 = 4^3/5 = 64/5`
a31 = `((3 + 1)^3)/5 = 4^3/5 = 64/5`
a32 = `((3 + 2)^3)/5 = 5^3/5 = 125/5`
∴ A = `[(8/5, 27/5),(27/5, 64/5),(64/5, 125/5)] = 1/5[(8, 27),(27,64),(64, 125)]`
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