We can rewrite as \mathbf{A} = \begin{bmatrix} b_1& c_1 & 0 &\dots & \dots &\dots \\ a_2 & b_2 & c_2 &\dots &\dots &\dots \\ & a_3 & b_3 & c_3 & \dots & \dots \\ & \dots & \dots &\dots &\dots & \dots \\ & & &a_{n-1} &b_{n-1}& c_{n-1} \\ & & & &a_n & b_n \\ \end{bmatrix} \begin{bmatrix} u_1\\ u_2\\ \dots \\ \dots \\ \dots \\ u_n\\ \end{bmatrix} =\begin{bmatrix} f_1\\ f_2\\ \dots \\ \dots \\ \dots \\ f_n\\ \end{bmatrix}.