How do I separate a column with a line within a matrix?

Question

I'm trying, without success, to separate a column or a row inside a matrix. What should I do in order to get the matrix in the picture?

Answer 1

Among many possibilities, here is an example with use of the nicematrix package:

\documentclass{article}
\usepackage{nicematrix}

\begin{document}
\[
\begin{bNiceArrayC}{CCC|C}
a_{11}  & \cdots    & a_{1n}    & b_1       \\
\vdots  & \ddots    & \vdots    & \vdots    \\
a_{n1}  & \cdots    & a_{nn}    & b_n       \\
\end{bNiceArrayC}
\]
\end{document}

Answer 2

I would do it with an array nested in a pmatrix:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{mathtools, bigstrut}

 \begin{document}%

\[ \begin{bmatrix}
\begin{array}{@{}cccc|c@{}}
     a_{11}&a_{12}& \cdots &a_{1n} & b_1 \bigstrut[t] \\
     \vdots & \vdots & \ddots& \vdots & \vdots \\
     a_{m1}&a_{n2}& \cdots &a_{mn} & b_n \bigstrut[b]
\end{array}\end{bmatrix} \]

\end{document} 

Answer 3

Also, a plain array:

\documentclass{article}
\begin{document}

\[
\left[\begin{array}{@{}ccc|c@{}}
a_{11}  & \cdots    & a_{1n}    & b_1       \\
\vdots  & \ddots    & \vdots    & \vdots    \\
a_{n1}  & \cdots    & a_{nn}    & b_n       \\
\end{array}\right]
\]

\end{document}