row echelon form

Morning!

Consider matrix  $$A = \begin{pmatrix} 1 & 1 & 1 & 1 & 1\\ 0 & 1 & 3 & 2 & 0\\ 1 & 1 & 0 & 5 & 1\\ 0 & 0 & 1 & -4 & 2\\ \end{pmatrix}$$

I want to find the row echolon form of A.

According to the solutions this is the first step toward that form.

$$\begin{pmatrix} 1 & 1 & 1 & 1 & 1\\ 0 & 1 & 3 & 2 & 0\\ 1 & 1 & 0 & 5 & 1\\ 0 & 0 & 1 & -4 & 2\\ \end{pmatrix} \sim \begin{pmatrix} 1 & 1 & 1 & 1 & 1\\ 0 & 1 & 3 & 2 & 0\\ 0 & 0 & 1 & -4 & 2\\ 0 & 0 & -1 & 4 & 0\\ \end{pmatrix}$$

It appear like  $$R_3-R_1 \mbox{ has been applied, but } R_3-R_1 \mbox{ is } \begin{pmatrix} 1&1&0&5&1 \end{pmatrix}-\begin{pmatrix} 1&1&1&1&1 \end{pmatrix} = \begin{pmatrix} 0&0&-1&4&0 \end{pmatrix}.$$

What have I been missing here?