How can I resolve a matrix of 13 rows and 40 columns?

I need to resolve an undeterminated matrix that corresponds to an Flux balance Analysis applied on Glicolysis pathway, I have 19 metabolites in the rows, and 40 fluxes in the columns. I want to know about its null space, rank, and space dimensions... Some programs? or any methods? Some ideas?

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It looks like part of your question got cut off. You can edit your question to put the rest in - click the "edit" button that is underneath the tags of your question. Also, it would be useful if you could explain more about where this problem is coming from. –  Zev Chonoles May 24 '12 at 0:17
Try online matrix calculators. There most certainly should be some. –  Nico Bellic May 24 '12 at 1:13
There are many all-purpose commercial mathematical programs that will handle this: Maple, Mathematica, Matlab, etc. There's a package called Linpack designed for linear algebra. I wouldn't be surprised to learn that Excel can handle this kind of problem. –  Gerry Myerson May 24 '12 at 1:16
There is also Octave, which is free, and should certainly be able to handle a $19 \times 40$ system of equations. –  copper.hat May 24 '12 at 3:01

You need to be a little more specific about what you want to achieve but here's something you could get started with:

Fire up Octave. Relevant Functions:

a = rand(19,40) %Just to get a random matrix to work with.
null(a) %Null space
rank(a) %Rank
rref(a) %Row Reduced Echelon Form


Anything else you need?

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Thank you so much!!! –  Cristian Velandia May 24 '12 at 7:36