Gaussian Elimination and Tridiagonal matrices, project 1

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.

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