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Construct an m × n matrix A = [a_{ij}], where a_{ij} is given by

a_{ij} = `("i" - 2"j")^2/2` with m = 2, n = 3

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#### Solution

To construct 2 × 3 matrices.

A = `["a"_"ij"]_(2 xx 3) = [("a"_11, "a"_12, "a"_13),("a"_2, "a"_22, "a"_23)]`

a_{11} = `(1 - 2 xx 1)^2/2`

= `(1 - 2)^2/2`

= `(- 1)^2/2`

= `1/2`

a_{12} = `(1 - 2 xx 2)^2/2`

= `(1 - 4)^2/2`

= `(- 3)^2/2`

= `9/2`

a_{13} = `(1 - 2 xx 3)^2/2`

= `(1 - 6)^2/2`

= `(- 5)^2/2`

= `25/2`

a_{21} = `(2 - 2 xx 1)^2/2`

= `(2 - 2)^2/2`

= `0/2`

= 0

a_{22} = `(2 - 2 xx 2)^2/2`

= `(2 - 4)^2/2`

= `(- 2)^2/2`

= `4/2`

= 2

a_{23} = `(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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