@Preben Alsholm 

How about this Matrix ?

your code have error for this Matrix A.

restart;

Sys:=[b1*u[1,2]*e^(I*(q*x1+k[1,2]*x1+phi1))+c1*u[1,3]*e^(I*(q*x1+k[1,3]*x1+phi1))-a2*u[2,1]*e^(I*(q*x1+k[2,1]*x1+phi2))-b2*u[2,2]*e^(I*(q*x1+k[2,2]*x1+phi2))-c2*u[2,3]*e^(I*(q*x1+k[2,3]*x1+phi2))-d2*u[2,4]*e^(I*(q*x1+k[2,4]*x1+phi2))=0,

b1*v[1,2]*e^(-I*(q*x1-k[1,2]*x1+phi1))+c1*v[1,3]*e^(-I*(q*x1-k[1,3]*x1+phi1))-a2*v[2,1]*e^(-I*(q*x1-k[2,1]*x1+phi2))-b2*v[2,2]*e^(-I*(q*x1-k[2,2]*x1+phi2))-c2*v[2,3]*e^(-I*(q*x1-k[2,3]*x1+phi2))-d2*v[2,4]*e^(-I*(q*x1-k[2,4]*x1+phi2))=0,

b1*(q+k[1,2])*u[1,2]*e^(I*(q*x1+k[1,2]*x1+phi1))+c1*(q+k[1,3])*u[1,3]*e^(I*(q*x1+k[1,3]*x1+phi1))-a2*(q+k[2,1])*u[2,1]*e^(I*(q*x1+k[2,1]*x1+phi2))-b2*(q+k[2,2])*u[2,2]*e^(I*(q*x1+k[2,2]*x1+phi2))-c2*(q+k[2,3])*u[2,3]*e^(I*(q*x1+k[2,3]*x1+phi2))-d2*(q+k[2,4])*u[2,4]*e^(I*(q*x1+k[2,4]*x1+phi2))=0,

b1*(-q+k[1,2])*v[1,2]*e^(-I*(q*x1-k[1,2]*x1+phi1))+c1*(-q+k[1,3])*v[1,3]*e^(-I*(q*x1-k[1,3]*x1+phi1))-a2*(q-k[2,1])*v[2,1]*e^(-I*(q*x1-k[2,1]*x1+phi2))-b2*(q-k[2,2])*v[2,2]*e^(-I*(q*x1-k[2,2]*x1+phi2))-c2*(q-k[2,3])*v[2,3]*e^(-I*(q*x1-k[2,3]*x1+phi2))-d2*(q-k[2,4])*v[2,4]*e^(-I*(q*x1-k[2,4]*x1+phi2))=0,

a2*u[2,1]*e^(I*(q*x2+k[2,1]*x2+phi2))+b2*u[2,2]*e^(I*(q*x2+k[2,2]*x2+phi2))+c2*u[2,3]*e^(I*(q*x2+k[2,3]*x2+phi2))+d2*u[2,4]*e^(I*(q*x2+k[2,4]*x2+phi2))-a3*u[3,1]*e^(I*(q*x2+k[3,1]*x2+phi3))-d3*u[3,4]*e^(I*(q*x2+k[3,4]*x2+phi3))=0,

a2*v[2,1]*e^(-I*(q*x2-k[2,1]*x2+phi2))+b2*v[2,1]*e^(-I*(q*x2-k[2,2]*x2+phi2))+c2*v[2,3]*e^(-I*(q*x2-k[2,3]*x2+phi2))+d2*v[2,4]*e^(-I*(q*x2-k[2,4]*x2+phi2))-a3*v[3,1]*e^(-I*(q*x2-k[3,1]*x2+phi3))-d3*v[3,4]*e^(-I*(q*x2-k[3,4]*x2+phi3))=0,

a2*(q+k[2,1])*u[2,1]*e^(I*(q*x2+k[2,1]*x2+phi2))+b2*(q+k[2,2])*u[2,2]*e^(I*(q*x2+k[2,2]*x2+phi2))+c2*(q+k[2,3])*u[2,3]*e^(I*(q*x2+k[2,3]*x2+phi2))+d2*(q+k[2,4])*u[2,4]*e^(I*(q*x2+k[2,4]*x2+phi2))-a3*(q+k[3,1])*u[3,1]*e^(I*(q*x2+k[3,1]*x2+phi3))-d3*(q+k[3,4])*u[3,4]*e^(I*(q*x2+k[3,4]*x2+phi3))=0,

a2*(-q+k[2,1])*v[2,1]*e^(-I*(q*x2-k[2,1]*x2+phi2))+b2*(-q+k[2,2])*v[2,2]*e^(-I*(q*x2-k[2,2]*x2+phi2))+c2*(-q+k[2,3])*v[2,3]*e^(-I*(q*x2-k[2,3]*x2+phi2))+d2*(-q+k[2,4])*v[2,4]*e^(-I*(q*x2-k[2,4]*x2+phi2))-a3*(-q+k[3,1])*v[3,1]*e^(-I*(q*x2-k[3,1]*x2+phi3))-d3*(-q+k[3,4])*v[3,4]*e^(-I*(q*x2+k[3,4]*x2+phi3))=0];

Var:=[b1,c1,a2,b2,c2,d2,a3,d3];

(A, v) := LinearAlgebra[GenerateMatrix]( Sys, Var );

plz help me

@Kitonum 

i want these equations. your code for my equations have error.

Sys:=[b1*u[1,2]*e^(I*(q*x1+k[1,2]*x1+phi1))+c1*u[1,3]*e^(I*(q*x1+k[1,3]*x1+phi1))-a2*u[2,1]*e^(I*(q*x1+k[2,1]*x1+phi2))-b2*u[2,2]*e^(I*(q*x1+k[2,2]*x1+phi2))-c2*u[2,3]*e^(I*(q*x1+k[2,3]*x1+phi2))-d2*u[2,4]*e^(I*(q*x1+k[2,4]*x1+phi2))=0,

b1*v[1,2]*e^(-I*(q*x1-k[1,2]*x1+phi1))+c1*v[1,3]*e^(-I*(q*x1-k[1,3]*x1+phi1))-a2*v[2,1]*e^(-I*(q*x1-k[2,1]*x1+phi2))-b2*v[2,2]*e^(-I*(q*x1-k[2,2]*x1+phi2))-c2*v[2,3]*e^(-I*(q*x1-k[2,3]*x1+phi2))-d2*v[2,4]*e^(-I*(q*x1-k[2,4]*x1+phi2))=0,

b1*(q+k[1,2])*u[1,2]*e^(I*(q*x1+k[1,2]*x1+phi1))+c1*(q+k[1,3])*u[1,3]*e^(I*(q*x1+k[1,3]*x1+phi1))-a2*(q+k[2,1])*u[2,1]*e^(I*(q*x1+k[2,1]*x1+phi2))-b2*(q+k[2,2])*u[2,2]*e^(I*(q*x1+k[2,2]*x1+phi2))-c2*(q+k[2,3])*u[2,3]*e^(I*(q*x1+k[2,3]*x1+phi2))-d2*(q+k[2,4])*u[2,4]*e^(I*(q*x1+k[2,4]*x1+phi2))=0,

b1*(-q+k[1,2])*v[1,2]*e^(-I*(q*x1-k[1,2]*x1+phi1))+c1*(-q+k[1,3])*v[1,3]*e^(-I*(q*x1-k[1,3]*x1+phi1))-a2*(q-k[2,1])*v[2,1]*e^(-I*(q*x1-k[2,1]*x1+phi2))-b2*(q-k[2,2])*v[2,2]*e^(-I*(q*x1-k[2,2]*x1+phi2))-c2*(q-k[2,3])*v[2,3]*e^(-I*(q*x1-k[2,3]*x1+phi2))-d2*(q-k[2,4])*v[2,4]*e^(-I*(q*x1-k[2,4]*x1+phi2))=0,

a2*u[2,1]*e^(I*(q*x2+k[2,1]*x2+phi2))+b2*u[2,2]*e^(I*(q*x2+k[2,2]*x2+phi2))+c2*u[2,3]*e^(I*(q*x2+k[2,3]*x2+phi2))+d2*u[2,4]*e^(I*(q*x2+k[2,4]*x2+phi2))-a3*u[3,1]*e^(I*(q*x2+k[3,1]*x2+phi3))-d3*u[3,4]*e^(I*(q*x2+k[3,4]*x2+phi3))=0,

a2*v[2,1]*e^(-I*(q*x2-k[2,1]*x2+phi2))+b2*v[2,1]*e^(-I*(q*x2-k[2,2]*x2+phi2))+c2*v[2,3]*e^(-I*(q*x2-k[2,3]*x2+phi2))+d2*v[2,4]*e^(-I*(q*x2-k[2,4]*x2+phi2))-a3*v[3,1]*e^(-I*(q*x2-k[3,1]*x2+phi3))-d3*v[3,4]*e^(-I*(q*x2-k[3,4]*x2+phi3))=0,

a2*(q+k[2,1])*u[2,1]*e^(I*(q*x2+k[2,1]*x2+phi2))+b2*(q+k[2,2])*u[2,2]*e^(I*(q*x2+k[2,2]*x2+phi2))+c2*(q+k[2,3])*u[2,3]*e^(I*(q*x2+k[2,3]*x2+phi2))+d2*(q+k[2,4])*u[2,4]*e^(I*(q*x2+k[2,4]*x2+phi2))-a3*(q+k[3,1])*u[3,1]*e^(I*(q*x2+k[3,1]*x2+phi3))-d3*(q+k[3,4])*u[3,4]*e^(I*(q*x2+k[3,4]*x2+phi3))=0,

a2*(-q+k[2,1])*v[2,1]*e^(-I*(q*x2-k[2,1]*x2+phi2))+b2*(-q+k[2,2])*v[2,2]*e^(-I*(q*x2-k[2,2]*x2+phi2))+c2*(-q+k[2,3])*v[2,3]*e^(-I*(q*x2-k[2,3]*x2+phi2))+d2*(-q+k[2,4])*v[2,4]*e^(-I*(q*x2-k[2,4]*x2+phi2))-a3*(-q+k[3,1])*v[3,1]*e^(-I*(q*x2-k[3,1]*x2+phi3))-d3*(-q+k[3,4])*v[3,4]*e^(-I*(q*x2+k[3,4]*x2+phi3))=0];

plz help me.

@Preben Alsholm 

thank you.

can i use that code for any Matrix?

@Carl Love 

no, i mean, for example x=-3 so, we can plot y[a] vs. y[b]

and also for another equation wa can plot y[a] vs. y[c].

and similary for another x.

that is a purpose.

how can i correlation between those?

@Carl Love 

i want rate of x between -3 ..3 and plot y[a], y[b], or y[c].

and i know their figure are 2D plot.

plz help me.

@Kitonum 

yes, you are right.

i make a mistake.

thank you for your help.

@Carl Love 

yes, you are right.

i make a mistake.

thank you for your help.

@Markiyan Hirnyk 

i have this Matrix:  A:=Matrix([[Matrix[[a,b],[c,d]]], [Matrix[[e,f],[g,h]]] ]).

so, i want this Matrix change to: A:=Matrix[[a,b,e,f],[c,d,g,h]].

plz help me

thank you

@Carl Love 

limits of integration is 0..1

dear @Kitonum 

for eight equations i use that algorithm but dont anser!

plz help me for eight equations.

1:  a1x1+b1x2+c1x3+d1x4+a2x5+b2x6+c2x7+d2x8=0;

2:  a1y1+b1y2+c1y3+d1y4+a2y5+b2y6+c2y7+d2y8=0;

.

.

.

8:  a1z1+b1z2+c1z3+d1z4+a2z5+b2z6+c2z7+d2z8=0.

thank you

@Kitonum 

thank you 

@Carl Love 

thank you