0
$\begingroup$

I am trying to solve the following system of equations in maple but it doesn't work for some reason:

solve({ a*(1-x)-x*f-x*e = 0,  b*(1-x)-x*c-x*d = 0,  c*(1-z)-z*b-z*a = 0,  d*(1-z)-z*e-z*f = 0,  e*(1-y)-y*d-y*c = 0,  f*(1-y)-y*a-y*b = 0,  a+b+c+d+e+f-1 = 0 }, {a, b, c, d, e, f }) 
  • 0
    I tried just now and for me, no answers in outputs, so, no solutions.2012-09-04

2 Answers 2

1

This linear system of equations is inconsistent. One way to see this is to recognize that the first 6 equations imply that the variables a to f all have value zero. But the last equation dictates that their sum is equal to 1. Clearly, if they are all zero then they cannot add up to 1.

eqs:=[a*(1-x)-x*f-x*e = 0,    b*(1-x)-x*c-x*d = 0,    c*(1-z)-z*b-z*a = 0,    d*(1-z)-z*e-z*f = 0,    e*(1-y)-y*d-y*c = 0,    f*(1-y)-y*a-y*b = 0,    a+b+c+d+e+f-1 = 0]:  vars:=[a, b, c, d, e, f]:  with(LinearAlgebra): 

Now compare results from

linsys:=GenerateMatrix(eqs[1..6],vars,augmented); LinearSolve(linsys);  LUDecomposition(GenerateMatrix(eqs[1..6],vars,augmented),output=R); %[1..-1,1..6].Vector(vars)=%[1..-1,7]; 

with that from,

linsys:=GenerateMatrix(eqs,vars,augmented); LinearSolve(linsys);  LUDecomposition(GenerateMatrix(eqs,vars,augmented),output=R); %[1..-1,1..6].Vector(vars)=%[1..-1,7]; 
0

The equations look linear in $a,b,c,d,e,f$. As such, you can use $A,b:=LinearAlgebra[GenerateMatrix](system\_of\_equations,variables);$ and then $LinearAlgebra[LinearSolve](A,b)$ to solve the matrix system.