Consider the general linear model Y = Xβ + ϵ, where E(ϵ) = 0. Let M=X〖(X^' X)〗^- X' denote the perpendicular projection

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Consider the general linear model Y = Xβ + ϵ, where E(ϵ) = 0. Let M=X〖(X^' X)〗^- X' denote the perpendicular projection matrix onto C(X) and denote by e ̂ the vector of residuals obtained from the least squares fit. Prove that β ̂ is least squares estimate of β if and only if e ̂⊥C(X).