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Question
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = `(("i" - "j")^2)/(5 - "i")`
Solution
A = [aij]3 × 2 = `[("a"_11, "a"_12),("a"_21, "a"_22),("a"_31, "a"_32)]`
Given that aij = `(("i" - "j")^2)/(5 - "i")`
∴ a11 = `((1 - 1)^2)/(5 - 1) = 0/4` = 0
a12 = `((1 - 2)^2)/(5 - 1) = 1/4`
a21 = `((2 - 1)^2)/(5 - 2) = 1/3`
a22 = `((2 - 2)^2)/(5 - 2) = 0/3` = 0
a31 = `((3 - 1)^2)/(5 - 3) = 4/2` = 2
a32 = `((3 - 2)^2)/(5 - 3) = 1/2`
∴ A = `[(0, 1/4),(1/3, 0),(2, 1/2)]`
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