\Large \[\left| A \right| = \left| {\begin{array}{*{31}{c}}
{{a_1}}&{{b_2}}&{{b_3}}& \cdots &{{b_n}}\\
{{c_2}}&{{a_1}}&0& \cdots &0\\
{{c_3}}&0&{{a_3}}& \cdots &0\\
\vdots & \vdots & \vdots &{}& \vdots \\
{{c_n}}&0&0& \cdots &{{a_n}}
\end{array}} \right|\]
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