## Generalised inverses – Solve normal equations

I am still not fully able to handle the concept of generalised inverses when applied to OLS. Is there a way to show that β = (X′X)−X′y+(Ik−(X′X)−X′X)z solves the normal equations: X′Xβ = X′y so that it holds for any z? Note: X is an (n × k)-regressor Answer AttributionSource : Link , Question Author : … Read more