MATLAB: 6 unknowns 6 equations PLS HELP ME!!

help

Hello, i have a term project but i cant do this project. Please help me. I must found l2 l3 m1 m3 n1 and n2 and i have to create 3×3 matrix with l1, m2,n3. This code give me too many solutions. Just for l2 is like 10 solutions.
    syms l2 l3 m1 m3 n1 n2;
l1= 1/2;
m2= 1/2;
n3=1;
eq1=((l1)^2)+((m1)^2)+((n1)^2) == 1;
eq2=((l2)^2)+((m2)^2)+((n2)^2) == 1;
eq3=((l3)^2)+((m3)^2)+((n3)^2) == 1;
eq4=(l1*l2)+(m1*m2)+(n1*n2) == 0;
eq5=(l1*l3)+(m1*m3)+(m1*n3) == 0;
eq6=(l2*l3)+(m2*m3)+(n2*n3) == 0;
eqns = [ eq1, eq2, eq3, eq4, eq5, eq6];
vars = [l2 l3 m1 m3 n1 n2];
[l2, l3, m1, m3, n1, n2] = vpasolve(eqns, vars); 
A=[l1 m1 n1; l2 m2 n2; l3 m3 n3];
    disp('Transformation Matrix=')
    disp(A)

Best Answer

The results you get are correct. Your equations are non-linear, so the solution involves the roots of the degree 8 polynomial 272*Z^8 - 160*Z^7 + 88*Z^6 - 360*Z^5 + 249*Z^4 + 72*Z^3 - 90*Z^2 + 9 = 0 . In the special case of polynomials, vpasolve() is defined to return all of the solutions.
All of the roots of that polynomial are complex. All roots of the system as a whole are complex: there are no real solutions for any of the variables. None of them can be said to be any "better" than the others to pick out just one.
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