# Backward Transformation

Backward Transformation (abbr. BTRAN). This applies to the factored system, $LaTeX: u E_1 E_2 \ldots E_n = c$, where each $LaTeX: E_i$ is an elementary matrix. The recursion is:
$LaTeX: u_n E_n = c$
$LaTeX: u_{n-1} E_{n-1} = u_n$
$LaTeX: u_{1} E_{1} = u_2$,
for which $LaTeX: u_1$ is a solution to the original system.