Question

Construct  a matrix A = `[a_("ij")]_(3 xx 2)` whose element a_ij is given by

a_ij = `((i - j)^2)/(5 - i)`

Answer 1

A = `[a_("ij")]_(3 xx 2)`

∴ A = `[(a_11, a_12),(a_21, a_22),(a_31, a_32)]`

a_ij = `((i - j)^2)/(5 - i)`

∴ a₁₁ = `(1 - 1)^2/(5 - 1) = 0, a_12 = (1 - 2)^2/(5 - 1) = (-1)^2/(4) = (1)/(4)`

a₂₁ = `(2 - 1)^2/(5 - 2) = (1)/(3), a_22 = (2 - 2)^2/(5 - 2)` = 0,

a₃₁ = `(3 - 1)^2/(5 - 3) = (2^2)/(2) = 2, a_32 = (3 - 2)^2/(5 - 3) = (1)/(2)`

∴ A = `[(0 ,1/4),(1/3, 0),(2, 1/2)]`.