# Backward substitution

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The recursion to solve a nonsingular upper triangular system, $LaTeX: Ux = b$. It starts with $LaTeX: x_n = b_n / U_{n,n}$, then

$LaTeX: x_j = \frac{1}{U_{j, j}} \left( b_j - \sum_{i > j} U_{i,j} x_i \right) \mbox{ for } j = n-1, \ldots ,1.$