Empty sym: 0-by-1 : Don't understand why

Hi,

I have the following problem :

I would like to solve this equation system but matlab doesn't find any solutions by sending the following message : Empty sym: 0-by-1

Do i need to adapt the code in a certain way or this system really doesn't have any solutions ?

Thank you for your help.

Regards,

Benoit

[Bruno Luong]

Why there is the comma?

3,981

Post your code (using Insert a Line of Code button) not the screen shot

[Walter Roberson]

The comma is causing the problem. You are effectively creating four equations,

3
981==EXPRESSION
10*pi==EXPRESSION
6283185.307==EXPRESSION

The first of those expressions, 3, cannot be solved to be equal to zero, so the solve() fails.

Answer 1

[Torsten]

I multiplied by the denominators and squared to get rid of the square roots.

Your system seems to have 4 (complex-valued) solutions.

syms Cs C2 Rl
R1 = 1000;
gm = 10;
eqns = [3.981*(gm*(2*Rl*C2+R1*Cs)+Cs) == gm*Rl*Cs*(1-gm*R1),...
        (10*pi*(gm*(2*Rl*C2+R1*Cs)+Cs))^2==2*gm*Rl*C2*Cs*(gm*R1+1),...
        6283185.307^2*(Rl*C2*Cs*(1+R1*gm))==2*gm];
S = solve(eqns,[Cs C2 Rl]);
format long
double(S.Cs)

ans = 
   1.0e-09 *

  0.005065552626999 + 0.318237745447037i
 -0.005065552626999 - 0.318237745447037i
  0.005065552626999 - 0.318237745447037i
 -0.005065552626999 + 0.318237745447037i

double(S.C2)

ans = 4×1

1.0e-04 * -0.125571466971436 0.125571466971436 -0.125571466971436 0.125571466971436

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double(S.Rl)

ans = 
 -0.000201720156037 + 0.012672845866091i
 -0.000201720156037 + 0.012672845866091i
 -0.000201720156037 - 0.012672845866091i
 -0.000201720156037 - 0.012672845866091i

eqns_orig = [3.981 == gm*Rl*Cs*(1-gm*R1)/(gm*(2*Rl*C2+R1*Cs)+Cs),...
             10*pi==(2*gm*Rl*C2*Cs*(gm*R1+1))^(1/2)/(gm*(2*Rl*C2+R1*Cs)+Cs),...
             6283185.307==(2*gm/(Rl*C2*Cs*(1+R1*gm)))^(1/2)];
for i = 1:4
  double(subs(eqns_orig,[Cs C2 Rl],[S.Cs(i) S.C2(i) S.Rl(i)]))
end

ans = 1×3

0 0 0

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ans = 1×3

0 0 0

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ans = 1×3

0 0 0

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ans = 1×3

0 0 0

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[Benoît]

Thank for your answer.

It is now solving the system but i shouldn't be obtaining complex solutions so i think there is a problem in my equations.

But thanks for the correction.