An un-summarized change.

scratch.page

@@ -77,4 +77,38 @@ v_1\\ \vdots \\ v_n
 \end{matrix}\right) = \left(\begin{matrix}
 rv_1 \\ \vdots \\ rv_n
 \end{matrix}\right)
+$$
+
+This system:
+$$\begin{alignedat}{4}
+ x & {}-{} &  y & {}+{} &  z & = 1\\
+3x & {}+{} &    &       &  z & = 3\\
+5x & {}-{} & 2y & {}+{} & 3z & = 5
+\end{alignedat}$$
+
+reduces
+
+$$
+\left(\begin{array}{rrr|r}
+1&-1&1&1\\
+3&0&1&3\\
+5&-2&3&5\\
+\end{array}\right) \longrightarrow_{-5\rho_1+\rho_3}^{-3\rho_1+\rho_2}
+\left(\begin{array}{rrr|r}
+1&-1&1&1\\
+0&3&-2&0\\
+0&3&-2&0\\
+\end{array}\right) \longrightarrow^{-\rho_2+\rho_3}
+\left(\begin{array}{rrr|r}
+1&-1&1&1\\
+0&3&-2&0\\
+0&0&0&0\\
+\end{array}\right)
+$$
+
+to a one parameter solution set:
+
+$$
+\{ \begin{pmatrix}1\\ 0\\ 0\end{pmatrix} +
+   \begin{pmatrix}-1/3\\ 2/3\\ 1\end{pmatrix} z \mid z \in \Bbb{R} \}
 $$