Problem with solution seemingly simple linear system of equations [0x1 sym]

Question

Jan Tomaszewski 2021-4-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/803946-problem-with-solution-seemingly-simple-linear-system-of-equations-0x1-sym

评论： Jan Tomaszewski 2021-4-16

Hi, I have a problem with solve linear system of equations. Every time I got a solution = 0x1 sym.Could anyone tell what's wrong with my code?

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d=32; %mm - Srednica tłoka

p1=0.585; %N/mm^2

p2=0.4;

F1=p1*pi*d^2/4;%N sila nacisku

F2=p2*pi*d^2/4;%N sila nacisku

L=[230 200 180 160 140 120 100 80 60 40]';

x_p1=[2.7 2.5 2.4 2.3 2.2 2.1 2 1.9 1.8 1.7]';

M1=F1*[L]*1e-3;%Nm

M2=F2*[L]*1e-3;%Nm

digits(8)

syms x1 x2

eqns=[F1*x1+M1*x2==x_p1]

xx=solve(eqns,[x1 x2])

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Answer 1

Stephan 2021-4-16

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/803946-problem-with-solution-seemingly-simple-linear-system-of-equations-0x1-sym#answer_676716

在 MATLAB Online 中打开

rewriting the system to matrix shows that this system has no solution, due to inconsistence:

d=32; %mm - Srednica tłoka
p1=0.585; %N/mm^2
p2=0.4;
F1=p1*pi*d^2/4;%N sila nacisku 
F2=p2*pi*d^2/4;%N sila nacisku 
L=[230 200 180 160 140 120 100 80 60 40]';
x_p1=[2.7 2.5 2.4 2.3 2.2 2.1 2 1.9 1.8 1.7]';
M1=F1*L*1e-3;%Nm
M2=F2*L*1e-3;%Nm
digits(8)
syms x1 x2 
eqns=F1*x1+M1*x2
A = equationsToMatrix(eqns)
sol = linsolve(A, x_p1)

gives:

A =
 
[ (3744*pi)/25, (21528*pi)/625]
[ (3744*pi)/25,  (3744*pi)/125]
[ (3744*pi)/25, (16848*pi)/625]
[ (3744*pi)/25, (14976*pi)/625]
[ (3744*pi)/25, (13104*pi)/625]
[ (3744*pi)/25, (11232*pi)/625]
[ (3744*pi)/25,  (1872*pi)/125]
[ (3744*pi)/25,  (7488*pi)/625]
[ (3744*pi)/25,  (5616*pi)/625]
[ (3744*pi)/25,  (3744*pi)/625]
 
Warning: Solution does not exist because the system is inconsistent. 
> In symengine
  In sym/privBinaryOp (line 1030)
  In sym/linsolve (line 63)
  In Untitled (line 15) 
 
sol =
 
 Inf
 Inf