How do you get rref with a variable in the last column?

[OFFLINEX]

I'm trying to figure out how to set up a matrix where I don't know the last value ex a+2+4=x, b+4+6=x, c+2+6=x.
Would it be something like this?
[1,0,0,x-6]
[0,1,0,x-10]
[0,0,1,x-8]

 

[HallsofIvy]

Are you missing some parameters in your equations?
You have "a+2+4=x, b+4+6=x, c+2+6=x" which I would just write as a+ 6= x, b+ 10= x, and c+ 8= x.

Assuming these are equations to be solve for a, b, and c, for given x, then they are exactly the same as a= x- 6, b= x- 10, and c= x- 8 which are already solved for a, b, and c in terms of x.

If you really want to write them in terms of the "augmented matrix", yes, it would be
\begin{bmatrix}1 & 0 & 0 & x- 6 \\ 0 & 1 & 0 & x- 10 \\ 0 & 0 & 1 & x- 8\end{bmatrix}
which is already "row reduced".