\par Here is an example with solving equation using the Gauss elimination method\newline
\emph{Example: Solve this system of linear equations using the method of gaussian elimination} \cite{Analyze-math}\newline
\begin{equation}
\left\{
\begin{array}{lcl}
x + y - z & = & -3 \\
-x + 3y + 2z & = & 5 \\
x + 5z & = & 9
\end{array}
\right.
\end{equation}
\emph{first i will start to write it in operation row}
\begin{equation}
A
\begin{pmatrix}
1 & 1 & - 1 \\
-1 & 3 & 2 \\
1 & 5 & 0
\end{pmatrix}
X
\begin{pmatrix}
x \\ y \\ z \\
\end{pmatrix}
B
\begin{pmatrix}
-3 \\ 5 \\ 9 \\
\end{pmatrix}
\end{equation}
\\
\begin{enumerate}
\item First you can write it in augmented matrix
\begin{equation}
\begin{bmatrix}
1 & 1 & - 1 &|& -3\\
-1 & 3 & 2 &|& 5 \\
1 & 0 & 5 &|& 9
\end{bmatrix}
\end{equation}
\item Add (1) to row (2) \textcolor{red}{$R_1+R_2$}
\begin{equation}
\begin{bmatrix}
1 & 1 & - 1 &|& -3\\
0 & 4 & 1 &|& 2 \\
1 & 0 & 5 &|& 9
\end{bmatrix}
\end{equation}
\item Add -1 times row (1) to row (3)
\[
\begin{equation}
\begin{bmatrix}
1 & 1 & - 1 &|& -3\\
0 & 4 & 1 &|& 2 \\
0 & -1 & 6 &|& 12
\end{bmatrix}
\color{red}{\begin{matrix}
\\
\\
R_3 - R_1\\}
\end{matrix}
\end{equation}
\item Interchange rows (2) and (3)
\[\begin{bmatrix}
1 & 1 & - 1 &|& -3\\
0 & -1 & 6 &|& 12\\
0 & 4 & 1 &|& 2
\end{bmatrix}
\color{red}{\begin{matrix}
\\
R_3\\
R_2\\
\end{matrix}}\]
\item Add 4 times row (2) to row (3)
\[ \begin{bmatrix}
1 & 1 & - 1 &|& -3\\
0 & -1 & 6 &|& 12\\
0 & 0 & 25 &|& 50
\end{bmatrix}
\color{red}{\begin{matrix}
\\
\\
R_3 + 4R_2\\
\end{matrix}}\]
\item Multiply all terms in row (2) by -1
\[ \begin{bmatrix}
1 & 1 & - 1 &|& -3\\
0 & 1 & - 6 &|& - 12\\
0 & 0 & 25 &|& 50
\end{bmatrix}
\color{red}{\begin{matrix}
\\
-R_2\\
\\
\end{matrix}}\]
And finally:
\item Multiply all terms in row (3) by 1/25
\[\begin{bmatrix}
1 & 1 & - 1 &|& -3\\
0 & 1 & - 6 &|& - 12\\
0 & 0 & 1 &|& 2
\end{bmatrix}
\color{red}{\begin{matrix}
\\
\\
(1/25)R_3\\
\end{matrix}}\]
我使用 TeX Studio。我尝试给 pmatrix 提供一个数字，但它没有接受。它说你忘记了一个额外的 '}' 我的代码有什么问题？+
答案1
在删除代码中的错误（虚假\]等；请参阅问题下方的评论）并使用该nicematrix包后，我将您的文档示例重写为以下 MWE（最小工作示例）：
\documentclass{article}
\usepackage{geometry} % enable to write all document example on one page
\usepackage{xcolor}
\usepackage{nicematrix}
\begin{document}
\begingroup
\NiceMatrixOptions{code-for-last-col = \color{red}}
%%%%
Here is an example with solving equation using the Gauss elimination method\newline
\emph{Example: Solve this system of linear equations using the method of Gaussian elimination} \cite{Analyze-math}
\begin{equation}
\setlength\arraycolsep{1pt}
\left\{
\begin{array}{lcr}
x + y - z & = & -3 \\
-x + 3y + 2z & = & 5 \\
x + 5z & = & 9
\end{array}
\right.
\end{equation}
\emph{first i will start to write it in operation row}
\begin{equation}
A \begin{pNiceArray}{RRR}
1 & 1 & -1 \\
-1 & 3 & 2 \\
1 & 5 & 0
\end{pNiceArray}
X \begin{pNiceArray}{RRR}
x \\ y \\ z \\
\end{pNiceArray}
B \begin{pNiceArray}{RRR}
-3 \\ 5 \\ 9 \\
\end{pNiceArray}
\end{equation}
\begin{enumerate}
\item First you can write it in augmented matrix
\begin{equation}
\begin{bNiceArray}{RRRCR}
1 & 1 & - 1 &|& -3 \\
-1 & 3 & 2 &|& 5 \\
1 & 0 & 5 &|& 9
\end{bNiceArray}
\end{equation}
\item Add (1) to row (2) \textcolor{red}{$R_1+R_2$}
\begin{equation}
\begin{bNiceArray}{RRRCR}
1 & 1 & - 1 &|& -3 \\
0 & 4 & 1 &|& 2 \\
1 & 0 & 5 &|& 9
\end{bNiceArray}
\end{equation}
\item Add -1 times row (1) to row (3)
\begin{equation}
\begin{bNiceArray}{RRRCR}[last-col]
1 & 1 & - 1 &|& -3 & \\
0 & 4 & 1 &|& 2 & \\
0 & -1 & 6 &|& 12 & R_3 - R_1
\end{bNiceArray}
\end{equation}
\item Interchange rows (2) and (3)
\[
\begin{bNiceArray}{RRRCR}[last-col]
1 & 1 & -1 &|& -3 & \\
0 & -1 & 6 &|& 12 & R_3 \\
0 & 4 & 1 &|& 2 & R_2
\end{bNiceArray}
\]
\item Add 4 times row (2) to row (3)
\[
\begin{bNiceArray}{RRRCR}[last-col]
1 & 1 & -1 &|& -3 & \\
0 & -1 & 6 &|& 12 & \\
0 & 0 & 25 &|& 50 & R_3 + 4R_2
\end{bNiceArray}
\]
\item Multiply all terms in row (2) by -1
\[
\begin{bNiceArray}{RRRCR}[last-col]
1 & 1 & -1 &|& -3 & \\
0 & 1 & -6 &|& -12 & -R_2 \\
0 & 0 & 25 &|& 50 &
\end{bNiceArray}
\]
\item And finally multiply all terms in row (3) by 1/25
\[
\begin{bNiceArray}{RRRCR}[last-col]
1 & 1 & -1 &|& - 3 & \\
0 & 1 & -6 &|& -12 & \\
0 & 0 & 1 &|& 2 & (1/25)R_3
\end{bNiceArray}
\]
\end{enumerate}
\endgroup
\end{document}
从您的文档示例中可以看出，您只对前五个矩阵进行了编号。上面的 MWE 遵循此编号。如果您希望对所有矩阵进行编号，那么在其余矩阵中，您需要分别将\[和替换\]为\begin{equation}和\end{equation}。
使用包bNiceArray中定义的nicematrix可以更简洁地将带有标签的矩阵写入行，这表明已执行的操作。
为了获得上述结果，您需要至少编译 MWE 两次。