Matrix equation solution keep giving only structure of the array not the value

new =
 
[ (29*y2)/5 - (7*z2)/10, 7*z2, -7*y2]
 
>> dif=MRA-Mprll

dif =

   -0.1337   -9.7234    1.3349

>> syms y2 z2
>> eqn = new - dif ==0 ;
>> solve(eqn)

ans = 

  struct with fields:

    y2: [0×1 sym]
    z2: [0×1 sym]

Answer 1

[John D'Errico]

As I explained in my comment to @Vasishta Bhargava, this is a problem with 3 equations, but only 2 unknowns. It is known as an over-determined problem. As such, it likely never has an exact solution, so solve cannot solve it.

Typically, one might use a tool like a linear regression, to find y2 and z2 that will minimize the errors in the three equations at once. I'll be lazy here and just use fminsearch.

new = @(yz) [(29*yz(1))/5 - (7*yz(2))/10, 7*yz(2), -7*yz(1)];
dif = [-0.1337   -9.7234    1.3349];
obj = @(yz) norm(new(yz) - dif);

yz = fminsearch(obj,[1 1])
yz =
        -0.190698528012633         -1.38904515739705

How well did it work?

[new(yz);dif]
ans =
        -0.133719852295332         -9.72331610177938          1.33488969608843
                   -0.1337                   -9.7234                    1.3349

quite well in fact.

I could also have use a direct linear regression.

[A,B] = equationsToMatrix(eqn);
double(A)\double(B)
ans =
        -0.190698604595212
         -1.38905731126807

So the same answer, but this time it is more precise, since fminsearch uses a tolerance.