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Question
Construct an m × n matrix A = [aij], where aij is given by
aij = `("i" - 2"j")^2/2` with m = 2, n = 3
Solution
To construct 2 × 3 matrices.
A = `["a"_"ij"]_(2 xx 3) = [("a"_11, "a"_12, "a"_13),("a"_2, "a"_22, "a"_23)]`
a11 = `(1 - 2 xx 1)^2/2`
= `(1 - 2)^2/2`
= `(- 1)^2/2`
= `1/2`
a12 = `(1 - 2 xx 2)^2/2`
= `(1 - 4)^2/2`
= `(- 3)^2/2`
= `9/2`
a13 = `(1 - 2 xx 3)^2/2`
= `(1 - 6)^2/2`
= `(- 5)^2/2`
= `25/2`
a21 = `(2 - 2 xx 1)^2/2`
= `(2 - 2)^2/2`
= `0/2`
= 0
a22 = `(2 - 2 xx 2)^2/2`
= `(2 - 4)^2/2`
= `(- 2)^2/2`
= `4/2`
= 2
a23 = `(2 - 2 xx 3)^2/2`
= `(2 - 6)^2/2`
= `(- 4)^2/2`
= `16/2`
= 8
∴ The required 2 × 3 martix is A = `[(1/2, 9/2, 25/2),(0, 2, 8)]`
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