How to find the solution for the system of equations

Question

Chandrashekar D S 2020-11-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/657928-how-to-find-the-solution-for-the-system-of-equations

回答： Arin 2022-10-14

I am trying to find the value of 14 variables using 14 system of equation but i am not getting the answer using solve() command (this is the value: val =Empty sym: 0-by-1 I am getting )

I have decalred lambda as 14x1 sym

lambda = sym('lambda', [14 1]) ;
%having contraint as lambda>=0
lambda =
 
  lambda1
  lambda2
  lambda3
  lambda4
  lambda5
  lambda6
  lambda7
  lambda8
  lambda9
 lambda10
 lambda11
 lambda12
 lambda13
 lambda14
 
 equ=[65*lambda8 - 102*lambda2 - 121*lambda3 - 126*lambda4 - 114*lambda5 - 88*lambda6 - 150*lambda7 - 113*lambda1 + 85*lambda9 + 91*lambda10 + 60*lambda11 + 74*lambda12 + 29*lambda13 + 51*lambda14 + 1 == 0...
 ,78*lambda8 - 116*lambda2 - 106*lambda3 - 128*lambda4 - 96*lambda5 - 96*lambda6 - 140*lambda7 - 102*lambda1 + 62*lambda9 + 78*lambda10 + 56*lambda11 + 76*lambda12 + 34*lambda13 + 58*lambda14 + 1 == 0...
 ,67*lambda8 - 106*lambda2 - 130*lambda3 - 133*lambda4 - 123*lambda5 - 92*lambda6 - 160*lambda7 - 121*lambda1 + 93*lambda9 + 98*lambda10 + 64*lambda11 + 78*lambda12 + 30*lambda13 + 53*lambda14 + 1 == 0...
, 84*lambda8 - 128*lambda2 - 133*lambda3 - 149*lambda4 - 123*lambda5 - 108*lambda6 - 170*lambda7 - 126*lambda1 + 86*lambda9 + 99*lambda10 + 68*lambda11 + 88*lambda12 + 37*lambda13 + 64*lambda14 + 1 == 0...
 ,60*lambda8 - 96*lambda2 - 123*lambda3 - 123*lambda4 - 117*lambda5 - 84*lambda6 - 150*lambda7 - 114*lambda1 + 90*lambda9 + 93*lambda10 + 60*lambda11 + 72*lambda12 + 27*lambda13 + 48*lambda14 + 1 == 0...
 , 64*lambda8 - 96*lambda2 - 92*lambda3 - 108*lambda4 - 84*lambda5 - 80*lambda6 - 120*lambda7 - 88*lambda1 + 56*lambda9 + 68*lambda10 + 48*lambda11 + 64*lambda12 + 28*lambda13 + 48*lambda14 + 1 == 0...
, 90*lambda8 - 140*lambda2 - 160*lambda3 - 170*lambda4 - 150*lambda5 - 120*lambda6 - 200*lambda7 - 150*lambda1 + 110*lambda9 + 120*lambda10 + 80*lambda11 + 100*lambda12 + 40*lambda13 + 70*lambda14 + 1 == 0...
 ,65*lambda1 + 78*lambda2 + 67*lambda3 + 84*lambda4 + 60*lambda5 + 64*lambda6 + 90*lambda7 - 53*lambda8 - 37*lambda9 - 49*lambda10 - 36*lambda11 - 50*lambda12 - 23*lambda13 - 39*lambda14 + 1 == 0...
, 85*lambda1 + 62*lambda2 + 93*lambda3 + 86*lambda4 + 90*lambda5 + 56*lambda6 + 110*lambda7 - 37*lambda8 - 73*lambda9 - 71*lambda10 - 44*lambda11 - 50*lambda12 - 17*lambda13 - 31*lambda14 + 1 == 0...
 ,91*lambda1 + 78*lambda2 + 98*lambda3 + 99*lambda4 + 93*lambda5 + 68*lambda6 + 120*lambda7 - 49*lambda8 - 71*lambda9 - 74*lambda10 - 48*lambda11 - 58*lambda12 - 22*lambda13 - 39*lambda14 + 1 == 0...
, 60*lambda1 + 56*lambda2 + 64*lambda3 + 68*lambda4 + 60*lambda5 + 48*lambda6 + 80*lambda7 - 36*lambda8 - 44*lambda9 - 48*lambda10 - 32*lambda11 - 40*lambda12 - 16*lambda13 - 28*lambda14 + 1 == 0...
, 74*lambda1 + 76*lambda2 + 78*lambda3 + 88*lambda4 + 72*lambda5 + 64*lambda6 + 100*lambda7 - 50*lambda8 - 50*lambda9 - 58*lambda10 - 40*lambda11 - 52*lambda12 - 22*lambda13 - 38*lambda14 + 1 == 0...
 ,29*lambda1 + 34*lambda2 + 30*lambda3 + 37*lambda4 + 27*lambda5 + 28*lambda6 + 40*lambda7 - 23*lambda8 - 17*lambda9 - 22*lambda10 - 16*lambda11 - 22*lambda12 - 10*lambda13 - 17*lambda14 + 1 == 0...
, 51*lambda1 + 58*lambda2 + 53*lambda3 + 64*lambda4 + 48*lambda5 + 48*lambda6 + 70*lambda7 - 39*lambda8 - 31*lambda9 - 39*lambda10 - 28*lambda11 - 38*lambda12 - 17*lambda13 - 29*lambda14 + 1 == 0]
 
 lambda_val = solve(equ,[lambda]);
 %% But its not giving any value for lambda

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Stephan 2020-11-23

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/657928-how-to-find-the-solution-for-the-system-of-equations#answer_553038

编辑：Stephan 2020-11-23

在 MATLAB Online 中打开

Your system is inconstistent and therefore there is no solution:

% x is shorter than lambda
x = sym('x', [14 1]) ;
% system as equations
equ=[65*x(8) - 102*x(2) - 121*x(3) - 126*x(4) - 114*x(5) - 88*x(6) - 150*x(7) - 113*x(1) + 85*x(9) + 91*x(10) + 60*x(11) + 74*x(12) + 29*x(13) + 51*x(14) + 1 == 0;
    78*x(8) - 116*x(2) - 106*x(3) - 128*x(4) - 96*x(5) - 96*x(6) - 140*x(7) - 102*x(1) + 62*x(9) + 78*x(10) + 56*x(11) + 76*x(12) + 34*x(13) + 58*x(14) + 1 == 0;
    67*x(8) - 106*x(2) - 130*x(3) - 133*x(4) - 123*x(5) - 92*x(6) - 160*x(7) - 121*x(1) + 93*x(9) + 98*x(10) + 64*x(11) + 78*x(12) + 30*x(13) + 53*x(14) + 1 == 0;
    84*x(8) - 128*x(2) - 133*x(3) - 149*x(4) - 123*x(5) - 108*x(6) - 170*x(7) - 126*x(1) + 86*x(9) + 99*x(10) + 68*x(11) + 88*x(12) + 37*x(13) + 64*x(14) + 1 == 0;
    60*x(8) - 96*x(2) - 123*x(3) - 123*x(4) - 117*x(5) - 84*x(6) - 150*x(7) - 114*x(1) + 90*x(9) + 93*x(10) + 60*x(11) + 72*x(12) + 27*x(13) + 48*x(14) + 1 == 0;
    64*x(8) - 96*x(2) - 92*x(3) - 108*x(4) - 84*x(5) - 80*x(6) - 120*x(7) - 88*x(1) + 56*x(9) + 68*x(10) + 48*x(11) + 64*x(12) + 28*x(13) + 48*x(14) + 1 == 0;
    90*x(8) - 140*x(2) - 160*x(3) - 170*x(4) - 150*x(5) - 120*x(6) - 200*x(7) - 150*x(1) + 110*x(9) + 120*x(10) + 80*x(11) + 100*x(12) + 40*x(13) + 70*x(14) + 1 == 0;
    65*x(1) + 78*x(2) + 67*x(3) + 84*x(4) + 60*x(5) + 64*x(6) + 90*x(7) - 53*x(8) - 37*x(9) - 49*x(10) - 36*x(11) - 50*x(12) - 23*x(13) - 39*x(14) + 1 == 0;
    85*x(1) + 62*x(2) + 93*x(3) + 86*x(4) + 90*x(5) + 56*x(6) + 110*x(7) - 37*x(8) - 73*x(9) - 71*x(10) - 44*x(11) - 50*x(12) - 17*x(13) - 31*x(14) + 1 == 0;
    91*x(1) + 78*x(2) + 98*x(3) + 99*x(4) + 93*x(5) + 68*x(6) + 120*x(7) - 49*x(8) - 71*x(9) - 74*x(10) - 48*x(11) - 58*x(12) - 22*x(13) - 39*x(14) + 1 == 0;
    60*x(1) + 56*x(2) + 64*x(3) + 68*x(4) + 60*x(5) + 48*x(6) + 80*x(7) - 36*x(8) - 44*x(9) - 48*x(10) - 32*x(11) - 40*x(12) - 16*x(13) - 28*x(14) + 1 == 0;
    74*x(1) + 76*x(2) + 78*x(3) + 88*x(4) + 72*x(5) + 64*x(6) + 100*x(7) - 50*x(8) - 50*x(9) - 58*x(10) - 40*x(11) - 52*x(12) - 22*x(13) - 38*x(14) + 1 == 0;
    29*x(1) + 34*x(2) + 30*x(3) + 37*x(4) + 27*x(5) + 28*x(6) + 40*x(7) - 23*x(8) - 17*x(9) - 22*x(10) - 16*x(11) - 22*x(12) - 10*x(13) - 17*x(14) + 1 == 0;
    51*x(1) + 58*x(2) + 53*x(3) + 64*x(4) + 48*x(5) + 48*x(6) + 70*x(7) - 39*x(8) - 31*x(9) - 39*x(10) - 28*x(11) - 38*x(12) - 17*x(13) - 29*x(14) + 1 == 0];
% Return a linear system as matrix
[A,b] = equationsToMatrix(equ)
% solve the linear system
lambda = A\b