Let the General Linear Model be represented by

y = Xß + u u ~ N(0,σ2I)

whereXisn x pnon-stochastic and of rankpand letß = (XtX)-1Xtybe the OLS estimate ofß.

Now suppose that certain linear constraints are known to hold between various elements of the parameter vectorß, i.e. there is ap x kmatrixRand ak x1 vectorqsuch thatRtß = q, wherek < p. Determine the Least Squares estimator ofßif the usual sum of squared residuals (y - Xß)t(y - Xß) is minimised with the added constraints thatRtß = q.