Suppose X and W are any two matrices with n rows for which C(X ) = C(W).

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Question:

Suppose X and W are any two matrices with n rows for which C(X ) = C(W). Show that Px = Pw. (Hint: (a) It is equivalent to (Px - Pw)'(Px - Pw) = 0. (b) For any vector v E C(X ), Pxv = v.)