Question

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

Answer 1

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)]`