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本帖最后由 青青子衿 于 2019-12-13 22:00 编辑 \begin{align*}
\begin{vmatrix}
a_{\overset{\,}{11}}&a_{\overset{\,}{12}}&a_{\overset{\,}{13}}\\
a_{\overset{\,}{21}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}&a_{\overset{\,}{23}}\\
a_{\overset{\,}{31}}&a_{\overset{\,}{32}}&a_{\overset{\,}{33}}\\
\end{vmatrix}=
\dfrac{\begin{vmatrix}
\,\begin{vmatrix}
a_{\overset{\,}{11}}&a_{\overset{\,}{12}}\\
a_{\overset{\,}{21}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}\\
\end{vmatrix}
&\begin{vmatrix}
a_{\overset{\,}{12}}&a_{\overset{\,}{13}}\\
\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}&a_{\overset{\,}{23}}\\
\end{vmatrix}\,\\
\,\begin{vmatrix}
a_{\overset{\,}{21}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}\\
a_{\overset{\,}{31}}&a_{\overset{\,}{32}}\\
\end{vmatrix}&\begin{vmatrix}
\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}&a_{\overset{\,}{23}}\\
a_{\overset{\,}{32}}&a_{\overset{\,}{33}}\\
\end{vmatrix}\,\\
\end{vmatrix}}{\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}}
\end{align*}
\begin{align*}
\begin{vmatrix}
a_{\overset{\,}{11}}&a_{\overset{\,}{12}}&a_{\overset{\,}{13}}&a_{\overset{\,}{14}}\\
a_{\overset{\,}{21}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{23}}}}&a_{\overset{\,}{24}}\\
a_{\overset{\,}{31}}&\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{32}}}}&\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{33}}}}&a_{\overset{\,}{34}}\\
a_{\overset{\,}{41}}&a_{\overset{\,}{42}}&a_{\overset{\,}{43}}&a_{\overset{\,}{44}}\\
\end{vmatrix}=
\dfrac{\begin{vmatrix}
\,\begin{vmatrix}
a_{\overset{\,}{11}}&a_{\overset{\,}{12}}&a_{\overset{\,}{13}}\\
a_{\overset{\,}{21}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{23}}}}\\
a_{\overset{\,}{31}}&\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{32}}}}&\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{33}}}}
\end{vmatrix}
&\begin{vmatrix}
a_{\overset{\,}{12}}&a_{\overset{\,}{13}}&a_{\overset{\,}{14}}\\
\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{23}}}}&a_{\overset{\,}{24}}\\
\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{32}}}}&\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{33}}}}&a_{\overset{\,}{34}}\\
\end{vmatrix}\,\\
\,\begin{vmatrix}
a_{\overset{\,}{21}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{23}}}}\\
a_{\overset{\,}{31}}&\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{32}}}}&\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{33}}}}\\
a_{\overset{\,}{41}}&a_{\overset{\,}{42}}&a_{\overset{\,}{43}}\\
\end{vmatrix}&\begin{vmatrix}
\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{23}}}}&a_{\overset{\,}{24}}\\
\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{32}}}}&\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{33}}}}&a_{\overset{\,}{34}}\\
a_{\overset{\,}{42}}&a_{\overset{\,}{43}}&a_{\overset{\,}{44}}\\
\end{vmatrix}\,\\
\end{vmatrix}}{\begin{vmatrix}
\,\,\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{22}}}}&\boxed{\bbox[cyan,2.2pt]{a_{\overset{\,}{23}}}}\,\,\\
\,\,\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{32}}}}&\boxed{\bbox[yellow,2.2pt]{a_{\overset{\,}{33}}}}\,\,\\
\end{vmatrix}}
\end{align*} |
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