solve symbol four equations for c1 c2 c3 c4

how can I solve these four equations for c1 c2 c3 c4

syms c1 c2 c3 c4 a b
T1=c1+c2*a+c3*b+c4*a*b;
T2=c1-c2*a+c3*b-c4*a*b;
T3=c1-c2*a-c3*b+c4*a*b;
T4=c1+c2*a-c3*b-c4*a*b;
 

Answer 1

[jannat alsaidi]

Thanks, I solve it,

clc
clear
syms a b x y c1 c2 c3 c4 T1 T2 T3 T4  
T=c1+c2*x+c3*y+c4*x*y;

%%
r1=c1+c2*a+c3*b+c4*a*b-T1;
r2=c1-c2*a+c3*b-c4*a*b-T2;
r3=c1-c2*a-c3*b+c4*a*b-T3;
r4=c1+c2*a-c3*b-c4*a*b-T4;

%%Find C1 and C4
p13=r1+r3;
p24=r2+r4;

n1=solve(p13==0,c1);
n2=solve(p24==0,c1);
C4=solve(n1==n2,c4)

w1=solve(p13==0,c4);
w2=solve(p24==0,c4);
C1=solve(w1==w2,c1)

r1=subs(r1,c1,C1);
r1=subs(r1,c4,C4);
r2=subs(r2,c1,C1);
r2=subs(r2,c4,C4);
r3=subs(r3,c1,C1);
r3=subs(r3,c4,C4);
r4=subs(r4,c1,C1);
r4=subs(r4,c4,C4);

%%Find C3
q12=r1+r2;
q34=r3+r4;
C3=solve(q12==0,c3)

r1=subs(r1,c3,C3);
r2=subs(r2,c3,C3);
r3=subs(r3,c3,C3);
r4=subs(r4,c3,C3);

%% find C2
C2=solve(r1==0,c2)

r1=subs(r1,c2,C2);
r2=subs(r2,c2,C2);
r3=subs(r3,c2,C2);
r4=subs(r4,c2,C2);
C1
C2
C3
C4

Answer 2

[KALYAN ACHARJYA]

solve here

[jannat alsaidi]

it does not worked with me

syms c1 c2 c3 c4 a b r1 r2 r3 r4
T1=c1+c2*a+c3*b+c4*a*b;
T2=c1-c2*a+c3*b-c4*a*b;
T3=c1-c2*a-c3*b+c4*a*b;
T4=c1+c2*a-c3*b-c4*a*b;
 
eqns=[T1==r1; T2==r2; T3==r3; T4==r4 ]
[c1 c2 c3 c4]=solve(eqns,[c1 c2 c3 c4])