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I have the following system of equations that I need to solve:

ArrayOfEquations={-(u/10) + 0.4 v[1] - 0.16 v[2] + 0.064 v[3] - 0.0256 v[4] + 
0.01024 v[5] - 0.004096 v[6] + 0.0016384 v[7] - 0.00065536 v[8] + 
0.000262144 v[9] == g[1], 
-0.4 v[1] + 0.32 v[2] - 0.192 v[3] + 0.1024 v[4] - 
0.0512 v[5] + 0.024576 v[6] - 0.0114688 v[7] + 0.00524288 v[8] - 
0.0023593 v[9] == g[2], 
-0.16 v[2] + 0.192 v[3] - 0.1536 v[4] + 0.1024 v[5] - 
0.06144 v[6] + 0.0344064 v[7] - 0.0183501 v[8] + 0.00943718 v[9] ==g[3], 
-0.064 v[3] + 0.1024 v[4] - 0.1024 v[5] + 0.08192 v[6] - 
0.057344 v[7] + 0.0367002 v[8] - 0.0220201 v[9] == g[4], 
-0.0256 v[4] + 0.0512 v[5] - 0.06144 v[6] + 0.057344 v[7] - 
0.0458752 v[8] + 0.0330301 v[9] == g[5], 
-0.01024 v[5] + 0.024576 v[6] - 0.0344064 v[7] + 
0.0367002 v[8] - 0.0330301 v[9] == g[6], 
-0.004096 v[6] + 0.0114688 v[7] - 0.0183501 v[8] + 
0.0220201 v[9] == g[7], 
-0.0016384 v[7] + 0.00524288 v[8] - 0.00943718 v[9] == g[8], 
-0.00065536 v[8] + 0.0023593 v[9] == g[9], 
-0.000262144 v[9] == g[10]}

I want to solve it for variables $u$ and $v[i]$, $i=1,..9$. When I call

Solve[ArrayOfEquations, Join[{u}, Array[v, 9]]]

I get {} as an output.

Why doesn't it work?

I understand that {} in general means no solution. However, I tried it with some numbers substituted for g[i] and got a numerical output. Can't understand what goes wrong if I keep the g[i] symbolically

Thanks for any help!

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  • $\begingroup$ ToRules@Reduce[ArrayOfEquations, Join[{u}, Array[v, 9]]] $\endgroup$ – Dr. belisarius May 15 '14 at 13:28
  • $\begingroup$ ...or add ,Reals as an option at the end $\endgroup$ – gpap May 15 '14 at 13:30
  • $\begingroup$ @belisarius I don't understand the output if I give your code line. For example, if I put Solve[ArrayOfEquations[[10]], v[9]], then I get v[9] -> -3814.7 g[10]. However, with your solution I get a different expression. Where do all the other terms come from? From the last equation, it's clear that for v[9] the answer is simple... $\endgroup$ – GregVoit May 15 '14 at 13:32
  • $\begingroup$ @gpap the same output as from belisarius... $\endgroup$ – GregVoit May 15 '14 at 13:33
  • $\begingroup$ Please see (for example)mathematica.stackexchange.com/a/18706/193 $\endgroup$ – Dr. belisarius May 15 '14 at 13:35
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Your equations are actually inconsistent unless $g$ has a particular form.

When I rationalise and solve, I obtain the following requirements on the solution

{True,
 7.10543*10^-15 g[7] + 7.10543*10^-15 g[8] + 7.10543*10^-15 g[9] == 0, 
 3.55271*10^-15 g[6] + 5.68434*10^-14 g[9] == 0,
 True,
 True, 
 1.11022*10^-16 g[6] + 8.88178*10^-16 g[7] + 3.55271*10^-15 g[8] + 7.10543*10^-15 g[9] == 0,
 True, True, True, True}

As others have said, this is a rounding error problem: when you substitute numerical values for g, those small terms will become very close to 0..

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