0
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A = Exp[-I*x] - Exp[-I*fi] Exp[I*x];
B2 = a21 + Exp[-I*x]*a20;
C2 = Cos[Theta] (a10 - a20);
DD = Exp[-2 I*fi] Exp[-I*x] - Exp[-I*fi] Exp[I*x];
B1 = Exp[-2 I*fi] (a11 - a10*Exp[-I*x]);
C1 = Cos[Theta] (a00 - a20);
EE = Exp[-I*fi] Exp[-I*x] - Exp[I*x];
B0 = Exp[-I*fi] (a01 - a00*Exp[-I*x]);
C0 = Cos[Theta] (a20 - a10);
Solve[
  F2 == (B2 + C2 + Cos[Theta]*(F0 - F1))/A & 
  F1 == (B1 + C1 + Cos[Theta]*(F2 - F0))/D & 
  F0 == (B0 + C0 + Cos[Theta]*(F1 - F2))/E, 
  {F1, F2, F0}]

Solve::nsmet: This system cannot be solved with the methods available to Solve. >>

What's the problem?

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closed as off-topic by Michael E2, xyz, MarcoB, Bob Hanlon, m_goldberg Sep 10 '15 at 2:53

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Michael E2, xyz, MarcoB, Bob Hanlon, m_goldberg
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory tour now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. $\endgroup$ – bbgodfrey Sep 10 '15 at 1:37
  • 1
    $\begingroup$ This error message means that Solve does not know how to solve this set of equations. Indeed, many equations do not have closed-for solutions. Would it meet your needs to obtain a numerical answer? $\endgroup$ – bbgodfrey Sep 10 '15 at 1:38
  • 2
    $\begingroup$ I think you want And instead of Function -- i.e, && instead of &. $\endgroup$ – Michael E2 Sep 10 '15 at 1:45
  • 1
    $\begingroup$ I think you want DD in that denominator and not D $\endgroup$ – Bill Sep 10 '15 at 2:26
1
$\begingroup$

Rewriting your code with & corrected to && and with parameters given in a more consistent manner

B0 = Exp[-I*fi] (a01 - a00*Exp[-I*x]);
B1 = Exp[-2 I*fi] (a11 - a10*Exp[-I*x]);
B2 = a21 + Exp[-I*x]*a20;
C0 = Cos[Theta] (a20 - a10);
C2 = Cos[Theta] (a10 - a20);
C1 = Cos[Theta] (a00 - a20);
AA = Exp[-I*x] - Exp[-I*fi] Exp[I*x];
DD = Exp[-2 I*fi] Exp[-I*x] - Exp[-I*fi] Exp[I*x];
EE = Exp[-I*fi] Exp[-I*x] - Exp[I*x];

Short[
  Solve[
    F2 == (B2 + C2 + Cos[Theta]*(F0 - F1))/AA &&
    F1 == (B1 + C1 + Cos[Theta]*(F2 - F0))/DD && 
    F0 == (B0 + C0 + Cos[Theta]*(F1 - F2))/EE,
    {F1, F2, F0}], 
  6]

gives the following solution:

solution

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