Homework Help: Proving partitioned matrix involving conditional inverse

1. Jul 27, 2010

cielo

1. The problem statement, all variables and given/known data

For matrix X partitioned as $$\underline{X}$$ = [ $$\underline{X}$$1 $$\underline{X}$$2 ] with $$\underline{X}$$1 matrix full column rank rx,

2. Relevant equations
prove that $$\underline{X}$$($$\underline{X}$$'$$\underline{X}$$)$$^{C}$$$$\underline{X}$$ = $$\underline{X'}$$$$_{1}$$'($$\underline{X'}$$$$_{1}$$$$\underline{X}$$$$_{1}$$)$$^{-1}$$$$\underline{X'}$$$$_{1}$$

3. The attempt at a solution
I would like to, but I don't have an idea how to solve this problem. I hope somebody can help me here.

Last edited: Jul 28, 2010