Click for printer friendely version of this HowTo . $${({\bf Y} - {\bf X}\hat{\boldsymbol{\beta}})' \left\{{\bf X}({\bf... ...} \right]^{-1}(\boldsymbol{\theta} - {\bf C}\hat{\boldsymbol{\beta}}) \right\}}$$ $$= ({\bf Y} - {\bf X}\hat{\boldsymbol{\beta}})' \left\{ {\bf X}({\bf... ... C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}} \right\}$$ $$= {\bf Y}'{\bf X}({\bf X}'{\bf X})^{-1}{\bf C}'[{\bf C}({\bf X}'{\b... ... C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}}$$ $$- \hat{\boldsymbol{\beta}}'{\bf X}'{\bf X} ({\bf X}'{\bf X})^{-1}... ... C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}}$$ $$= \hat{\boldsymbol{\beta}}'{\bf C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\... ... C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}}$$ $$- \hat{\boldsymbol{\beta}}' {\bf C}'[{\bf C}({\bf X}'{\bf X})^{-1... ... C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}}$$ $$=$$ 0

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