Gauss solver for linear system of the equations

function fundam - is the solver of system of linear equations

call [C,D,rank]=fundam(A_num,A_den) see Execute.m for examples.
A_num, A_den - two matrices which set the coefficients (numerators,denominators) of the linear equation system.

For example
1/2*x1-2/3*x2=5/4
3/4*x1+5/7*x2=2/1
A_num=[1 -2 5; 3 5 2]
A_den=[2 3 4;4 7 1]

there are 3 category of results:
1) System is inconsystent
2) System is consistent and has еру only one common solution
3) System is consystent and has a lot of solutions

The output of the solver are the matrices of the coeficients C,D - have the same logic (numerators and denominators) of each coefficient near Xn.

for 2) category (one common solution) C always has diagonal form

For example:
Numerators
C= [1 0 3;
0 1 2]

Denominators
D=[1 1 1;
1 1 5]

means
X1 =3
X2=2/5

for 3) category matrices C,D represents the fundamental solution for the system

for example

Numerators
C= [1 2 3]

Denominators
D=[1 1 7;]

should be accounted as fundamental solution:

1*X1+2*X2=3/7

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rank is rank ;)