# Why the result of my code is empty matrices?

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Faezeh Manesh on 6 Apr 2021
Hi,
I am trying to solve a system of nonlinear equations using the folowing code. When I run my code it gives me empty matrices. Can someone help me why this happens and how I can fix this problem?
clc
clear all
syms a1 a2 a3 b1 b2 b3 c1 c2 c3
a3=0;
b3=0;
m1=0.894;
m2=0.894;
m3=1.252;
eq1 = a1*a2+b1*b2+c1*c2==0;
eq2 = a2*a3+b2*b3+c2*c3==0;
eq3 = a1*a3+b1*b3+c1*c3==0;
eq4 = (a1)^2+(b1)^2+(c1)^2==1;
eq5 = (a2)^2+(b2)^2+(c2)^2==1;
eq6 = (a3)^2+(b3)^2+(c3)^2==1;
M1=[a1*a1 a1*b1 a1*c1;a1*b1 b1*b1 b1*c1;a1*c1 b1*c1 c1*c1];
M2=[a2*a2 a2*b2 a2*c2;a2*b2 b2*b2 b2*c2;a2*c2 b2*c2 c2*c2];
M3=[a3*a3 a3*b3 a3*c3;a3*b3 b3*b3 b3*c3;a3*c3 b3*c3 c3*c3];
M = m1*M1+m2*M2+m3*M3;
eq7 = det(M)==1;
eqns = [eq1 eq2 eq3 eq4 eq5 eq6 eq7];
vars = [a1 a2 b1 b2 c1 c2 c3];
[S_a1, S_a2, S_b1, S_b2, S_c1, S_c2, S_c3] = solve(eqns,vars);
Thanks,
Faezeh
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