(OLS) Let E[y | X] = X 0 and Var[y | X] = 0 where 0 R k , X is full-row

(OLS) Let E[y | X] = Xβ₀ and Var[y | X] = Ω₀ where β₀ ∈ R^k, X is full-row rank, and Ω₀ is nonsingular. Show that for all c ∈ R^k.

directly from these expressions for the variance matrices. (HINT: Use the Cholesky decomposition of Ω₀ to express this difference in terms of an orthogonal projection matrix.)

Var[e Bots IX] - Var[e'CALS |X] - [(XX) 'XQX(XX)-(XX