MHB Complete augmented by row operations

[karush]

$\left[ \begin{array}{rrrr|r} 1& -5& 4& 0&0\\ 0& 1& 0& 1&0\\ 0& 0& 3& 0&0\\ 0& 0& 0& 2&0 \end{array}\right] $ OK my first move on this is $r_3/3$ and $r_4/2$. $\left[ \begin{array}{rrrr|r} 1& -5& 4& 0&0\\ 0& 1& 0& 1&0\\ 0& 0& 1& 0&0\\ 0& 0& 0& 1&0 \end{array}\right]$ $r_2-r_4=r_2\quad$ doesn't this whole thing zero out?

 

[skeeter]

yep ... reduced row-echelon form is

$\begin{bmatrix}
1 & 0 & 0 & 0 &0\\
0 & 1 & 0 &0 &0 \\
0 & 0 & 1 & 0 &0 \\
0 & 0 & 0 & 1 & 0
\end{bmatrix}$