Trying to understand least squares estimates

[Nastya]

Hi, I'm trying to understand which mathematical actions I need to perform to be able to arrive at the solution shown in the uploaded picture. Thank you.

 

[mfb]

Are you just looking for the matrix multiplication? If not, I don't understand what you are asking.

 

[WWGD]

As a general statement, least squares allows you to obtain " best possible solutions " to systems like :

Ax=b , where b is not in the column space of A. This statement leads to a system like the one you attached to your post. You find the values of x that minimize the
$L^2$ distance $||Ax -b ||_2$, and this is the orthogonal projection of b onto Ax.

 

[Nastya]

Are you just looking for the matrix multiplication? If not, I don't understand what you are asking.

Yes, thank you. I will review the matrix multiplication.