证明
$$
\left|\begin{array}{lll}
a_1 & b_1 & c_1 \\
a_2 & b_2 & c_2 \\
a_3 & b_3 & c_3
\end{array}\right|=a_1\left|\begin{array}{ll}
b_2 & c_2 \\
b_3 & c_3
\end{array}\right|-b_1\left|\begin{array}{ll}
a_2 & c_2 \\
a_3 & c_3
\end{array}\right|+c_1\left|\begin{array}{ll}
a_2 & b_2 \\
a_3 & b_3
\end{array}\right|
$$