CODEWITHSUNDEEP
wolfram-mathematica
aiwass
aiwass

Reputation: 31

Issue solving linear system using Solve

I have a system of 4 linear equations in terms of variables that I have obtained from solving previous systems, but the Solve function does not return output despite it appearing to be a very straightforward system to solve:

Solve[{
 -d5c2 dn5t1 - d5c3 dn5t1 - a3 n3t1 - 
  (d4c1 n4t1 (dn4t2 n5t1 - dn4t1 n5t2))/(n4t2 n5t1 - n4t1 n5t2)
    ==  dn3t1,
 -a3 n3t2 - (d5c2 dn5t1 n5t2)/n5t1 - 
  (d5c3 dn5t1 n5t2)/n5t1 -
  (d4c1 n4t2 (dn4t2 n5t1 - dn4t1 n5t2))/(n4t2 n5t1 - n4t1 n5t2) 
    == dn3t2,
 -a3 n3t3 - 
  (d4c1 n4t3 (dn4t2 n5t1 - dn4t1 n5t2))/(n4t2 n5t1 - n4t1 n5t2) - 
  (d5c2 dn5t1 n5t3)/n5t1 - (d5c3 dn5t1 n5t3)/n5t1 
    ==  dn3t3,
 -a3 n3t4 - 
  (d4c1 n4t4 (dn4t2 n5t1 - dn4t1 n5t2))/(n4t2 n5t1 - n4t1 n5t2) -
  (d5c2 dn5t1 n5t4)/n5t1 - (d5c3 dn5t1 n5t4)/n5t1
    == dn3t4
       }, {a3, d5c2, d5c3, d4c1}]

Returns blank output: 

{}

I am new to the language; is there some kind of limit to the size of non-numerical expressions that Solve can handle or anything like that?

Upvotes: 2

Views: 265

Answers (1)

agentp
agentp

Reputation: 6989

Your system has no solution. It might be useful to show how to put this in canonical linear algebra form:

sys={
 -d5c2 dn5t1 - d5c3 dn5t1 - a3 n3t1 - 
  (d4c1 n4t1 (dn4t2 n5t1 - dn4t1 n5t2))/(n4t2 n5t1 - n4t1 n5t2)
    ==  dn3t1,
 -a3 n3t2 - (d5c2 dn5t1 n5t2)/n5t1 - 
  (d5c3 dn5t1 n5t2)/n5t1 -
  (d4c1 n4t2 (dn4t2 n5t1 - dn4t1 n5t2))/(n4t2 n5t1 - n4t1 n5t2) 
    == dn3t2,
 -a3 n3t3 - 
  (d4c1 n4t3 (dn4t2 n5t1 - dn4t1 n5t2))/(n4t2 n5t1 - n4t1 n5t2) - 
  (d5c2 dn5t1 n5t3)/n5t1 - (d5c3 dn5t1 n5t3)/n5t1 
    ==  dn3t3,
 -a3 n3t4 - 
  (d4c1 n4t4 (dn4t2 n5t1 - dn4t1 n5t2))/(n4t2 n5t1 - n4t1 n5t2) -
  (d5c2 dn5t1 n5t4)/n5t1 - (d5c3 dn5t1 n5t4)/n5t1
    == dn3t4
       }

lhs = sys[[All, 1]];
rhs = sys[[All, 2]];

(m = Transpose[Coefficient[lhs, #] & /@ {a3, d5c2, d5c3, d4c1}]) // MatrixForm

enter image description here

At this point you could try LinearSolve[m,rhs], however in this case it reports

Linear equation encountered that has no solution

And we see this is because the determinant is zero.

  Det[m]

0

fundamentally your unknowns d5c2 and d5c3 have the same coefficient in every equation, so you effectively have four equations and only three unknowns.

Upvotes: 3

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