# Column separation in math mode

I'm trying to put the following three equations into a matrix:

$$x_1 + 2x_2 = 7\\ -2x_1 + 5x_2 = 4\\ -5x_1 + 6x_2 = -3$$


When I use the following bmatrix:

$$\begin{bmatrix}1\;2\;7\\-2\;5\;4\\-5\;6\;-3\end{bmatrix}$$


the resulting matrix is a mess, with no real column separation. Is there a way to specify columns in math mode? I know about presetting column separation widths, but I would rather it be done automatically, rather than as a presetting.

In the LaTeX tabular and array environments, as well as in the matrix-like environments such as matrix, pmatrix, bmatrix, and vmatrix, the only widely recognized column separator character is &. If you replace all instances of \; with &, the resulting output will start to look much better.

To make the matrix at hand look really good, though, you may want to switch from using a bmatrix to a bmatrix* environment and impose right-alignment of the column contents. Plus, add a \phantom{-} directive to one of the cells in the middle column to balance the column widths.

\documentclass{article}
\usepackage{mathtools} % for 'bmatrix*' env.
\begin{document}
$\begin{bmatrix}1\;2\;7\\-2\;5\;4\\-5\;6\;-3\end{bmatrix} \quad\text{vs.}\quad \begin{bmatrix} 1&2&7\\-2&5&4\\-5&6&-3 \end{bmatrix} \quad\text{vs.}\quad \begin{bmatrix*}[r] 1&2&7\\-2&5&4\\-5&\phantom{-}6&-3 \end{bmatrix*}$
\end{document}


\documentclass{article}
\usepackage{amsmath}
\begin{document}

$M= \begin{bmatrix} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 5 & 7 & -3 \end{bmatrix}$

\end{document}


## OR

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}

$M= \begin{bmatrix*}[r] 1 & 2 & 3 \\ 3 & 4 & 5 \\ 5 & 7 & -3 \end{bmatrix*}$

\end{document}