Solving equations involving specific elements of matrices. Is this possible on MATLAB?

So lets say I have 2 matrices A and B. I need to solve 2 eqns involving specific elements of each matrix. e.g. A(1)+B(2)=4; A(1)-B(2)=2.

Is there any way to do this? My efforts with Fsolve and solve have failed. Here's what I've done so far:

    function F=myfun(A,B)
  F=[A(1)-B(2)-2;
     A(1)+B(2)-4]; 
  end

In the command window I typed:

>>A=ones(2,2);
>> B=ones(2,2);
>> [A,B]=fsolve(@myfun,A,B)

I even tried

[A(1),B(1)]=fsolve(@myfun,A(1),B(1))

Neither attempt worked.

Answer 1

[Matt J]

Since the equations are linear, you should just use MLDIVIDE

 x = [1 -1; 1 +1]\[2;4]

 A(1)=x(1);
 B(2)=x(2);

[Yagnaseni Roy]

This is just a simplified version (kind of a schematic representation) of the set of equations I'm trying to solve which are actually extremely complicated and non-linear!

[Matt J]

If you were to solve the linear equations in your example with FSOLVE, it would look like this

     function F=myfun(z)

       F = [1 -1; 1 +1]*z(:) - [2;4]

     end

and then something like,

 z=fsolve(@myfun,[1,1]);

If you then want the solution variables, z(i), placed inside specific matrix entries, you are free to do so by direct assignment, e.g.,

    A(1,1)=z(1);
    B(2,1)=z(2);