I want to make a matrix looks good in Overleaf. However, for some reason, the last entry is not centred. How to fix it? Also, in the inline mathematics expression, why I cannot bold the expression?

\documentclass[11pt,a4paper]{report}
\begin{document}
\usepackage{amsmath}
\begin{gather}
\textbf{Y} = 

\begin{pmatrix}
$\textbf{Y_1}$\\
$\textbf{Y_2}$\\
$\vdots$        \\
$\textbf{Y_S}$
\end{pmatrix},

\textbf{U} = 

\begin{pmatrix}
$\textbf{U_{1,s}}$\\
$\textbf{U_{2,s}}$\\
$\vdots$        \\
$\textbf{U_{10,s}}$
\end{pmatrix}, 

\textbf{$\beta$} = 

\begin{pmatrix}
$\beta_{0,s}$\\
$\beta_{1,s}$\\
$\vdots$        \\
$\beta_{10,s}$
\end{pmatrix},
\end{gather}
\end{document}

where

\textbf{$Y_s$} $= (y_{1,s}, y_{2,s}, …, y_{G, s})$, and $\textbf{$U_m$}$ $= 
(u_{1,m, s}, u_{2,m, s}, ..., u_{G,m, s}).$

It results like this

The variable beta should be bold, also Y_S and U_M after "where." Please help. Thank you