Suggest edit — Elimination Matricies

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---
title: "Elimination Matricies"
type: concept
source: https://www.jemoka.com/posts/kbhelimination_matrix/
confidence: high
status: active
---

For matrix \(A\), we want to make a series of matrix \(M\) which will zero columns out. This is a algorithms approach for doing this, which is also applied columnwise.
nicely, we can undo our operations
and you can compose them by subtracting together
*THIS IS ONLY TRUE when we are applying in the right ordering, row \(1\) to row \(2\), etc.
pivoting this procedure breaks on:
\begin{equation} A = \mqty(0 &amp; 4 \\ 4 &amp; 9) \end{equation}
because it requires dividing by \(\frac{1}{0}\); to &ldquo;fix&rdquo; this, reorder the equatinos.
you can flip both rows and columns.
partial pivoting: swap rows to use the largest magnitue element in the column under consideration full pivoting: swap rows and columns to use the largest element on the upper left Remember to change the order of \(b\) in the first case, and both \(b\) (rows) and \(c\) (columns) in the second case.