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答案1
计算正确;-)
\documentclass{article}
\usepackage{amsmath,mathtools}
\newcommand{\GE}[1]{%
\qquad\left\Updownarrow\;
\begin{aligned}#1\end{aligned}%
\right.%
}
\begin{document}
\begin{align*}
&\left[\begin{array}{@{}ccc|ccc@{}}
3 & -2 & 4 & 1 & 0 & 0 \\
1 & 0 & 2 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 & 0 & 1
\end{array}\right]
\\
&\GE{
R_3 & \leftrightarrow R_1 \\
R_2 & \leftrightarrow R_1
}
\\
&\left[\begin{array}{@{}ccc|ccc@{}}
1 & 0 & 2 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 & 0 & 1 \\
3 & -2 & 4 & 1 & 0 & 0
\end{array}\right]
\\
&\GE{
R_3 & \coloneqq R_2-3R_1 \\
R_3 & \coloneqq R_3+2R_1
}
\\
&\left[\begin{array}{@{}ccc|ccc@{}}
1 & 0 & 2 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 & 0 & 1 \\
0 & 0 & -2 & 1 & -3 & 2
\end{array}\right]
\end{align*}
\end{document}