# Request for open source program for finding reduced row echelon form of an augmented matrix

I have hundreds of augmented matrices in the following form: $$\left(\begin{array}{cccc|c} 1 & 1 & 1 & 1& 2+\frac{4}{f}\\ a & b & c & d& 2\\ p & q & r & s& 2\\ m & n & k & l & 2 \end{array}\right),$$ where $$a$$, $$b$$, $$c$$, $$d$$, $$p$$, $$q$$, $$r$$, $$s$$ are known and $$m$$, $$n$$, $$k$$, $$l$$ are not known.

For example, $$a=1$$, $$b=0$$, $$c=2$$, $$d=0$$, $$p=0$$, $$q=2$$, $$r=0$$ and $$s=2$$, we have $$\left(\begin{array}{cccc|c} 1 & 1 & 1 & 1& 2+\frac{4}{f}\\ 1 & 0 & 2 & 0& 2\\ 0 & 2 & 0 & 2& 2\\ m & n & k & l & 2 \end{array}\right).$$ Then I need to compute its rref as follows: $$\left(\begin{array}{cccc|c} 1 & 1 & 1 & 1& 2+\frac{4}{f}\\ 1 & 0 & 2 & 0& 2\\ 0 & 2 & 0 & 2& 2\\ m & n & k & l & 2 \end{array}\right) \rightarrow \left(\begin{array}{cccc|c} 1 & 0 & 0 & 0& \frac{8}{f}\\ 0 & 1 & 0 & 1& 1\\ 0 & 0 & 1 & 0& 1-\frac{4}{f}\\ 0 & 0 & 0 & l-n & -\frac{f(n+k-2)+8m-4k}{f} \end{array}\right)$$ I have tried Wolfram Alpha, but somehow it assumes $$l\neq n$$ even I insist $$l=n$$:

I have tried wxmaxima but it fails to do the task.

I would like to know whether there is any open source program to do the computation without assuming $$l\neq n$$.

• why don't you do simply wolframalpha.com/input/… ? Commented Apr 19, 2020 at 5:26
• Alternatively, you can add "assume" in front of "$l=n$" to get the same result. Commented Apr 19, 2020 at 5:27
• If you want to insist that $l=n$, why not just replace $l$ by $n$ ?
– Ted
Commented Apr 19, 2020 at 6:00
• If I replace $n$ by $l$ in wolframalpha as janmarqz did, I will get a trivial matrix without f. I want to find out the condition on f in terms of $m$, $n$, $k$, $l$ such that the system have infinite many solutions. Of course, I can do it by hand one by one. But hundreds of matrices spend me too much time and it is very easy to make mistakes. Commented Apr 19, 2020 at 7:24