Question: 19.5 Let PX and MX be as defined in Equations (19.24) and (19.25). a. Prove that PXMX = 0n * n and that PX and

19.5 Let PX and MX be as defined in Equations (19.24) and (19.25).

a. Prove that PXMX = 0n * n and that PX and MX are idempotent.

b. Derive Equations (19.27) and (19.28).

c. Show that rank(PX) = k + 1 and rank(MX) = n - k - 1. [Hint: First solve Exercise 19.10, and then use the fact that trace(AB) = trace(BA)

for conformable matrices A and B.]

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