Solve the system
$$\left\lbrace \begin{array}{r@{}r@{}r@{}r@{}r} > x_1 & - x_2 & - 6 x_3 & = & -5 \\ >2 x_1 & - 2 x_2 & - 4 x_3 & = & -8 \\ >2 x_1 & & + 8 x_3 & = & 3 >\end{array} \right.$$
$$\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix} = \begin{bmatrix}\\\\\\\end{bmatrix} +s \begin{bmatrix}\\\\\\\end{bmatrix}$$
My work so far
I solved the RREF form to get
$$\begin{bmatrix}1&0&0&\frac{1}{2}\\0&1&0&4\\0&0&1&\frac{1}{4}\end{bmatrix}$$
My assumption would be the row reduced form says
\begin{align*} x_1 & =\frac{1}{2}\\ x_2 & =4\\ x_3 & =\frac{1}{4}\\ \end{align*}
To get
$$\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix} = \begin{bmatrix}\frac{1}{2}\\4\\\frac{1}{4}\end{bmatrix} +s \begin{bmatrix}\\\\\\\end{bmatrix}$$
However, I'm unsure where to go from here. How would I get the solution for the $+s$ column? Also, is my work correct so far?