\left| \begin{array}{c c c c c}
a_1 & 0 & \dots & 0 & b_1 \\
0 & a_2 & \dots & 0 & b_2 \\
\vdots & \vdots & \ddots & \vdots & \vdots \\
 0 & 0 & \dots & a_{n - 1}& b_{n - 1} \\
 -a_n & -a_n & \dots & -a_n & b_n + a_n\\ \end{array} \right|