# Parentheses around a matrix

So this is the code that I have so far:

$Y = \begin{bmatrix} Y_{1} \\ Y_{2} \\ \vdots \\ Y_{n} \end{bmatrix} = \begin{bmatrix} 42 \\ 33 \\ 75 \\ 28 \\ 91 \\ 55 \end{bmatrix}\quad X= \begin{bmatrix} 1 & X_{11} & X_{12} & ... & & X_{1,p-1}\\ 1 & X_{21} & X_{22} & ... & & X_{2,p-1}\\ \vdots & \vdots & \vdots & & & \vdots\\ 1 & X_{n1} & X_{n2} & ... & & X_{n,p-1}\\ \end{bmatrix} = \begin{bmatrix} 1 & 7 & 33\\ 1 & 4 & 41\\ 1 & 16 & 7\\ 1 & 3 & 49\\ 1 & 21 & 5\\ 1 & 8 & 31 \end{bmatrix}$


And I want to write out this equation:

\textbf{b}=$(X'X)^{-1}(X'Y)$


I would like to put a parentheses around X'X, but how would I do that? like in this format:

([x][x'])<-big parentheses around matricies


Not exactly sure what you're after, but the following might be sufficient to show you what you can do:

\documentclass{article}

\usepackage{amsmath}

\newcommand{\Xmatrix}{
\begin{bmatrix}
1 &  7 & 33 \\
1 &  4 & 41 \\
1 & 16 &  7 \\
1 &  3 & 49 \\
1 & 21 &  5 \\
1 &  8 & 31
\end{bmatrix}}
\newcommand{\Ymatrix}{
\begin{bmatrix}
42 \\ 33 \\ 75 \\ 28 \\ 91 \\ 55
\end{bmatrix}}

\begin{document}

$Y = \begin{bmatrix} Y_1 \\ Y_2 \\ \vdots \\ Y_n \end{bmatrix} = \Ymatrix \quad X = \begin{bmatrix} 1 & X_{11} & X_{12} & \cdots & X_{1,p-1} \\ 1 & X_{21} & X_{22} & \cdots & X_{2,p-1} \\ \vdots & \vdots & \vdots & & \vdots \\ 1 & X_{n1} & X_{n2} & \cdots & X_{n,p-1} \\ \end{bmatrix} = \Xmatrix$

$\mathbf{b} = \bigl( X^T X \bigr)^{-1} \bigl( X^T Y \bigr)$

$\mathbf{b} = \left( \Xmatrix^T \Xmatrix \right)^{-1} \left( \Xmatrix^T \Ymatrix \right)$

$\mathbf{b} = \begin{pmatrix} \Xmatrix^T \Xmatrix \end{pmatrix}^{-1} \begin{pmatrix} \Xmatrix^T \Ymatrix \end{pmatrix}$

\end{document}


Large braces or brackets around objects can either be achieved using "\big operators", \left...\right pairs, or *matrix-like environments.