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How to solve 3 interconnected equations?

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Lu Da Silva
Lu Da Silva el 23 de Oct. de 2020
Comentada: Ameer Hamza el 23 de Oct. de 2020
I have a vecor R with 10 values
M = S * 3 and S = R+M
how do I connect the vector with the 2 equations in order to receive a vector M with 10 values and a vector S with 10 values?
Would a for-loop be a viable solution?

Respuestas (1)

Ameer Hamza
Ameer Hamza el 23 de Oct. de 2020
Editada: Ameer Hamza el 23 de Oct. de 2020
If you have symbolic toolbox, you can use solve()
syms M S R
Rv = rand(10, 1);
eq1 = M == S*3;
eq2 = S == R+M;
sol = solve([eq1; eq2], [M S]);
M_sol = subs(sol.M, Rv);
S_sol = subs(sol.S, Rv);
Result
>> M_sol
M_sol =
-14923794479723871/18014398509481984
-4255113867394491/4503599627370496
-108056045000625/2251799813685248
-16610538751653585/18014398509481984
-9792936758686299/18014398509481984
-1338449427099159/18014398509481984
-1653620415623073/2251799813685248
-5201938487820639/18014398509481984
-1662959758749849/9007199254740992
-694097603644977/2251799813685248
>> S_sol
S_sol =
-4974598159907957/18014398509481984
-1418371289131497/4503599627370496
-36018681666875/2251799813685248
-5536846250551195/18014398509481984
-3264312252895433/18014398509481984
-446149809033053/18014398509481984
-551206805207691/2251799813685248
-1733979495940213/18014398509481984
-554319919583283/9007199254740992
-231365867881659/2251799813685248
If you want floating-point answer
M_sol = double(M_sol);
S_sol = double(S_sol);
Reault
>> M_sol
M_sol =
-0.2198
-0.2836
-0.0640
-0.9528
-0.4228
-0.8079
-1.0427
-0.7487
-0.8037
-0.6678
>> S_sol
S_sol =
-0.0733
-0.0945
-0.0213
-0.3176
-0.1409
-0.2693
-0.3476
-0.2496
-0.2679
-0.2226
Alternatively use fsolve():
R = rand(10, 1);
eq = @(M,S) [M-S*3; S-(R+M)];
sol = fsolve(@(x) eq(x(1:10),x(11:20)), zeros(20, 1));
M_sol = sol(1:10);
S_sol = sol(11:20);
  2 comentarios
Lu Da Silva
Lu Da Silva el 23 de Oct. de 2020
Can I solve it without the use of any extra tools?
Ameer Hamza
Ameer Hamza el 23 de Oct. de 2020
For that, you will need to first solve the equations by hand. You will get
S = -R/2
M = -3R/2
and then use MATLAB
R = rand(10, 1);
S = -R/2
M = -3*R/2

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