Need help on simple linear regression proof

I want to derive the least square estimation of the coefficients for y=B_0+B_1*x_1+e

Can someone walk me through how to get from B to D in the image below?

http://i.imgur.com/9zwvO.jpg

I can do it through taking the derivative of the residual sum of squares, but I want to know how to do the proof through the general formula.

Re: Need help on simple linear regression proof

I'm going to call and , then, assuming no error, we have the equation , with the aim to solve for .

Normally, what could be done is to premultiply both sides by , but we can't do that in this case because is not a square matrix. But we can CREATE a square matrix by premultiplying both sides by first. This gives the equation .

Now that is a square matrix, to solve this equation for we need to premultiply both sides by , giving

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Re: Need help on simple linear regression proof

Edit. Thanks for the help, I solved the proof.