I have a question regarding Gauss Jordan Elimination. I have this matrix:
\begin{bmatrix}2&1&5&0\\1&0&-3&1\\7&2&2&1\end{bmatrix}
So at the start I will switch R1 with R2, like that is for me the most logical thing to do. But if I run the matrix through http://www.gregthatcher.com/Mathematics/GaussJordan.aspx They don't do it this way and get a different answer than I do. My answer is
\begin{bmatrix}1&0&0&7\\0&1&0&-24\\0&0&1&2\end{bmatrix}
and that is wrong. The answer should be
\begin{bmatrix}1&0&0&-5\\0&1&0&20\\0&0&1&-2\end{bmatrix}
Shouldn't I get the same answer in the end no matter how I do the reduction? I don't see anything wrong with my method. Can someone check my answer with my method ( start by switching R1 and R2) ?