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How to solve 3 interconnected equations?

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Lu Da Silva
Lu Da Silva on 23 Oct 2020
Commented: Ameer Hamza on 23 Oct 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?

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Answers (1)

Ameer Hamza
Ameer Hamza on 23 Oct 2020
Edited: Ameer Hamza on 23 Oct 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 Comments

Lu Da Silva
Lu Da Silva on 23 Oct 2020
Can I solve it without the use of any extra tools?
Ameer Hamza
Ameer Hamza on 23 Oct 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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