Question: (Partitioned Projection) Suppose that X = [X1, X2] is full-column rank. Show Px = X(XX) X=Px + (1-Px)P12 by showing that [Px + (1 -

(Partitioned Projection) Suppose that X = [X1, X2] is full-column rank. Show Px = X(XX) X=Px + (1-Px)P12 by showing that [Px + (1 - Px) P12] X = X (3.25) [Px (1-PxP12] x2 = X2 z'x 0 Vxe Col(X) = [Px+(I-Px, P12] z=0 where X = EX1, X21. Px, X (XX)X, and P12 is given in (3.13). Draw Pxy. Px.y, and (I-Px.)Pizy in a figure like Figure 3.13.

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