1.2.6 Determinant calculation

Problem: Calculate the determinant of the \( n \)-th order \[ \Delta=\left|\begin{array}{cccccc} 0 & a_{2} & a_{3} & \ldots & a_{n-1} & a_{n} \\ b_{1} & 0 & a_{3} & \ldots & a_{n-1} & a_{n} \\ b_{1} & b_{2} & 0 & \ldots & a_{n-1} & a_{n} \\ \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ b_{1} & b_{2} & b_{3} & \ldots & 0 & a_{n} \\ b_{1} & b_{2} & \ldots & \ldots & b_{n-1} & 0 \end{array}\right| . \]