Linear Algebra and the C Language/a04i

We can write:

       Input = Output
A = x1       = x2 + x3
B = x2 + x4  = x5  
C = x5 + x6  = x7
D = x3 + x7  = x8
E = x8       = x1 + x4 + x6

We write: x1 = 50; x3 = 20; x5 = 60; x8 = 90;

A = 50       = x2 + 20
B = x2 + x4  = 60  
C = 60 + x6  = x7
D = 20 + x7  = 90
E = 90       = 50 + x4 + x6 

Let's rectify the system

 -x2      = +20 -50
 +x2 +x4  = +60  
 +x6 -x7  = -60
 +x7      = +90 -20
 -x4 -x6  = +50 -90    

Now:

  x2   x4   x6   x7
 -x2   +0   +0   +0   +0   = +20 -50
 +x2  +x4   +0   +0   +0   = +60  
  +0   +0  +x6  -x7   +0   = -60
  +0   +0   +0  +x7   +0   = +90 -20
  +0  -x4  -x6   +0   +0   = +50 -90

The code in C language:

double ab[RA*(CA+Cb)]={
// x2    x4    x6    x7
   -1,   +0,   +0,   +0,   +0,    +20 -50,
   +1,   +1,   +0,   +0,   +0,    +60,  
   +0,   +0,   +1,   -1,   +0,    -60,
   +0,   +0,   +0,   +1,   +0,    +90 -20,
   +0,   -1,   -1,   +0,   +0,    +50 -90 
};

The solution is given by solving the system:

  x2    x4    x6    x7 
  +1    +0    +0    +0    +0   +30 
  +0    +1    +0    +0    +0   +30 
  +0    +0    +1    +0    +0   +10 
  +0    +0    +0    +1    +0   +70 
  +0    +0    +0    +0    +0    +0 

  x2 = +30;    x4 = +20;    x6 = +10;    x7 = +70;
  
  et x1 = 50; x3 = 20; x5 = 60; x8 = 90;