# linsolve consistency problem in system equation

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Emiliano Rosso on 10 Apr 2023
Hi
When I run this code I obtain a simple solution.
x=rand(1,3);
swc(1,1:3)=x+1;
syms x1 x2 x3;
eqn11=swc(1,1)==x1+1;
eqn12=swc(1,2)==x2+1;
eqn13=swc(1,3)==x3+1;
[A,B] = equationsToMatrix([eqn11,eqn12,eqn13], [x1,x2,x3]);
X = linsolve(A,B)
X =
1069854916266911/1125899906842624
77565677658637/2251799813685248
987964467329731/2251799813685248
x-X'
ans =
[ 0, 0, 0]
but when I run this I obtain an error :
x=rand(1,3);
swc(1,1:3)=x+1;
swc(2,1:3)=x+2;
swc(3,1:3)=x+3;
syms x1 x2 x3;
eqn11=swc(1,1)==x1+1;
eqn12=swc(1,2)==x2+1;
eqn13=swc(1,3)==x3+1;
eqn21=swc(2,1)==x1+2;
eqn22=swc(2,2)==x2+2;
eqn23=swc(2,3)==x3+2;
eqn31=swc(3,1)==x1+3;
eqn32=swc(3,2)==x2+3;
eqn33=swc(3,3)==x3+3;
[A,B] = equationsToMatrix([eqn11,eqn21,eqn31,eqn12,eqn22,eqn32,eqn13,eqn23,eqn33], [x1,x2,x3]);
X = linsolve(A,B)
Warning: solution does not exist because the system is inconsistent.
> In symengine
In sym/privBinaryOp (line 1034)
In sym/linsolve (line 63)
X =
Inf
Inf
Inf
The problem is that in this deliberately trivial example the lines are parallel 3 by 3 and therefore return the exact same value of x , so we should find ourselves in the case of a system of dependent but consistent equations. (following the link https://ionamaths.weebly.com/uploads/1/4/2/0/14204419/consistencyanddependency.pdf )
Why don't I obtain simply x as in the the previous example ???
Thanks!

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