If I have a matrix like this:
$$ \left[\begin{array}{rrrrrrrrr|r} 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & y_1-y_0 \\ 0 & 1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & y_0-y_1 \\ 0 & 0 & 1 & 1 & -1 & 0 & 0 & 0 & 0 & y_1-y_0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & y_2-y_1 \\ 0 & 0 & 0 & 0 & 1 & 2 & -1 & 0 & 0 & y_1-y_2 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & -1 & 0 & y_2-y_1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & y_3-y_2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 3 & 0 \\ \end{array}\right] \\ $$
How can I solve it using the tridiagonal algorithm? The first step in all of the versions of the algorithm that I have seen involve dividing by zero. For example: http://www.cfd-online.com/Wiki/Tridiagonal_matrix_algorithm_-TDMA(Thomas_algorithm)