Consider the binary variable version of the fixed effects model, except with an additional regressor 1ᵢ; that is
ᵢₜ = ₀ + 1xᵢₜ + ᵧ₁1ᵢ + ᵧ₂2ᵢ + ...... + ᵧₙᵢ + ᵢₜ.

Suppose that =3. Show that the binary regressors and the "constant" regressor are perfectly multicollinear; that is, express one of the variables 1ᵢ, 2ᵢ, 3ᵢ, and x₀, it as a perfect linear function of the others, where x₀,=1 for all i,t.