---
title: "Math 339SP -- Reduced row echelon form"
author: "Tim Chumley"
date: "Spring 2022"
output:
pdf_document: default
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(tinytex)
library(expm)
library(pracma)
```
# Reduced row echelon form
The commands below demonstrate how to do the row reduction that you saw
in linear algebra when solving systems of equations. On paper, you should
write out the system of equations and its augmented matrix. Then you can
input the augmented matrix, as done below, and run the `rref` command. It
is your job to interpret its output.
```{r}
A = matrix(c(-1/2, 1/3, 0,
1/2, -1/3, 0,
1, 1, 1), nrow = 3, ncol = 3, byrow = T) # an augmented matrix
rref(A) # the command to find its reduced row echelon form
```