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Thomas algorithm, backward substitution

The next step is the backward substitution step. The last row is multiplied by c_{N-3}/b_{N-2} and subtracted from the second to last row, thus eliminating c_{N-3} from the last row. The general backward substitution procedure is c_i = 0, and f_{i-1} = f_{i-1} - \frac{c_{i-1}}{b_i}f_i All that remains to be computed is the solution, which is the very straight forward process of x_i = \frac{f_i}{b_i}