# Proving partitioned matrix involving conditional inverse

## Homework Statement

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

## Homework Equations

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

## 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.

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