how to solve a system of linear equations (56 unknown Variables - 56 equations)

with regards , how to solve this system of linear equations ? (56 equations)

(unknown Variables are : b1 c1 d1 e1 g1 f1 s1 q1 b2 c2 d2 e2 g2 f2 s2 q2 b3 c3 d3 e3 g3 f3 s3 q3 b4 c4 d4 e4 g4 f4 s4 q4 b5 c5 d5 e5 g5 f5 s5 q5 b6 c6 d6 e6 g6 f6 s6 q6 b7 c7 d7 e7 g7 f7 s7 q7 )

Answer 1

[Walter Roberson]

One way is eliminating one variable at a time; see attached.

[Walter Roberson]

See also equationsToMatrix():

[A, b] = equationsToMatrix(eqns);
Bsol = A \ b;
[V(:), double(Bsol(:))]

Note that the result is notably different than

   Bsol = double(A) \ double(B)

which suggests that your equation is badly conditioned. Indeed,

rcond(double(A))

is around 2E-60 which indicates your system is near singular.

That in turn suggests that the round-off error inherent in your various constants is going to have a major difference in the results.

For example the very first number in your .txt is 1.035 . Does that represent 1035/1000 exactly ? Does it represent 1.0349999999999999200639422269887290894985198974609375 exactly, which is the nearest representable double precision number? Does it represent "some number between 1.0345 (inclusive) and 1.0355 (exclusive)" which has been rounded to 1.035 ? The choice between these for even just this one number could lead to a huge difference in the outputs.

[homa bayat]

Thank you so much my dear friend