What's the best way to create this formula with latex?

Question

I'm trying to create this formula (the one with the matrices) for my essay in latex but I'm having a hard time finding the best way of going about it.

Answer 1

The coding of this matrix product is quite straightforward, just take the time to write the four matrices that make up the formula with indexed variables.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
\begin{equation*}
  \begin{pmatrix}
    y_1 \\
    \vdots \\
    y_n
  \end{pmatrix}=
  \begin{pmatrix}
    1 & x_{12} & \ldots & x_{1k} \\
    \vdots & \vdots & \ddots & \vdots \\
    1 & x_{N2} & \ldots & x_{Nk}
  \end{pmatrix}
  \begin{pmatrix}
    \beta_1 \\
    \vdots \\
    \beta_k
  \end{pmatrix}
  +
  \begin{pmatrix}
    u_1 \\
    \vdots \\
    u_k
  \end{pmatrix}
\end{equation*}
% <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
\end{document}