I'm kind of new to MatLab and i'm trying to solve a Linear Algebra problem for my class of Linear Algebra of the course of Physics. Also, my first language is portuguese so forgive me for my not-so-perfect english.
I have a (solved) linear system of 7 equations and 12 variables (A, B, C, D, E, F, G, H, I, J, K, L) that is the following:
A = 33 - K - L
B = 1 + F - J
C = -15 - F + J + K + L
D = 15 + H - K
E = 16 - F - H + J + K
G = 34 - H - J - L
I = 18 - J - K
Note: I'm using letters (A, B, ..., L) instead of X1, X2, ..., X12 because it's easier to write it like this here and because I don't know if the Xn notation is allowed on Maple (i don't think so).
So, the system is possible but undetermined (with 5 degrees of freedom), being F, H, J, K and L the free variables.
Until here, everything's fine. The problem arises when the professor asks us for every solution of the system that satisfies the condition that all the variables (form A to L) are positive integers (A, B, C, D, E, F, G, H, I, J, K, L ϵ IN → natural numbers).
From my understanding, that gives rise to a system of linear inequalities with 12 variables and the following inequalities:
A = 33 - K - L > 0;
B = 1 + F - J > 0;
C = -15 - F + J + K + L > 0
D = 15 + H - K > 0
E = 16 - F - H + J + K > 0
G = 34 - H - J - L > 0
I = 18 - J - K > 0
F > 0
H > 0
J > 0
K > 0
L > 0 (and A,B,C,D,E,F,G,H,I,J,K,L ϵ IN)
After some research, i found that a possible way to solve this type of system of linear inequalities is trough a method of elimination (analog to Gauss-Jordan's elimination method for systems of linear equations) named Fourier-Motzkin. But it's hardwork and i wanted to do it on the computer. Is there a simple way to do it on MatLab?
I really need help solving this as the professor told us that the first one to solve it would win a book, hehe.
I would really apreciate an answer, as my only goal as a future physicist is to unveil the secrets of the Cosmos to us all.
Thank you again.