Question

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

a_ij = `(i + j)^3/(5)`

Answer 1

a_ij = `(i + j)^3/(5)`

∴ a11 =`(1 + 1)^3/(5) = (2^3)/(5) = (8)/(5), a_12 = (1 + 2)^3/(5) = (3^3)/(5) = (27)/(5)`

a₂₁ = `(2 + 1)^3/(5) = (3^3)/(5) = (27)/(5), a_22 = (2 + 2)^3/(5) = (4^3)/(5) = (64)/(5)`

a₃₁ = `(3 + 1)^3/(5) = (4^3)/(5) = (64)/(5), a_32 = (3 + 2)^3/(5) = (5^3)/(5) = (125)/(5)`

∴ A = `[((8)/(5), (27)/(5)),((27)/(5), (64)/(5)),((64)/(5),  25)]`