Given a matrix in row-reduced form, like



except usually bigger, and with fractional values: given that the variables x1...xn are integers greater than zero, is there a quick way to tell how many solutions there are? Quick is a relative term here; I don't mean quick when done manually, anything that runs in polynomial time would be awesome.

Thanks in advance!

why? so you could take over the world? NEVER!

Disregard this post. My roommate doesn't know what he's talking about.

You see the diagnol of zeroes? That's probably a really good indicator of how many zeroes are in the place, 3 in that matrix. If you have several, as long as you know none of the lines are multiples of the other matrices then i think you're set to saying those number of lines are the number of solutions.

The_Lost_One: Nothing gets by you, eh? Yes, this is an NP problem... but perhaps something that runs in really fast exponential time?

tinny: Huh? either you're working on a way higher level than me, or I'm just going nuts from lack of sleep and thus can't understand you...

Okay, new question: how would one change the number of nested loops, without using recursion?

The matrix is all around us....
If you are the one...











You will ask your math professor..

You'd usually have to change your approach entirely. The major feature of the best algorithms is that they bear no resemblance to the second best.

I have no idea what the your question is on about, but if you kind of start from the beginning explaining what you have to do I may be able to help.

I'm sorry, I meant diagnol of ones. Ok, its kind of tricky to do this but try to learn how to take the row echelon form of a matrix. You can find an example and steps on how to do this here:

http://algebra.math.ust.hk/linear_equation/04_echelon_form/lecture3.shtml

Once you've done that, all the number of non zero rows you have give you the number of solutions you will get

Thanks for the help guys; I don't really need it anymore seeing as the assignment was due an hour ago (I did get it done though). Now I'm going to go die; I stayed up all night working on it and I feel like crap.