We start with the linear set of equations $$ \mathbf{A}\mathbf{u} = \mathbf{f}, $$ where \( \mathbf{A} \) is a tridiagonal matrix which we rewrite as $$ \mathbf{A} = \begin{bmatrix} b_1& c_1 & 0 &\dots & \dots &\dots \\ a_2 & b_2 & c_2 &\dots &\dots &\dots \\ & a_3 & b_3 & c_3 & \dots & \dots \\ & \dots & \dots &\dots &\dots & \dots \\ & & &a_{n-1} &b_{n-1}& c_{n-1} \\ & & & &a_n & b_n \\ \end{bmatrix} $$ where \( a,b,c \) are one-dimensional arrays of length \( 1:n \). In project 1 the arrays \( a \) and \( c \) are equal, namely \( a_i=c_i=-1/h^2 \). The matrix is also positive definite.