

#include 
#include  // setw
#include    // abs

using namespace std;

const int N = 3;

double a [N][N] = { {1, 2, 3},
                    {1, 2, 1},
                    {3, 1, 2} };

double b [N] = {6, 3, 6};

string name [N] = { "x", "y", "z"};

void tisk ()
{
    int i,k;
    for (i=0; i= 0 )
         {
             cout << "+";
         }
         cout << a[i][k] << "*" << name[k] << " ";
     }
     cout << " = " << b[i] << endl;
    }
}

void deleni (int r, double q)
// r-tou radku delime cislem q
{
    for (int k = 0; k < N; k++)
    {
        a[r][k] = a[r][k]/q;

    }
    b [r] =  b [r]/q;
}

void odcitani (int c, int r, double f)
// od c-te radky odecitame f nasobek r-te radky
{
    for (int k = 0; k < N; k++)
    {
        a[c][k] = a[c][k] - a[r][k]*f;

    }
    b[c] =  b [c] - b[r]*f;
}

void swap (double & u, double & v)
{
    double t = u;
    u = v;
    v = t;
}

void prehod (int z, int r)
// prehodit z-tou a r-tou radku
{
    for (int k = 0; k < N; k++)
    {
        swap (a[z][k], a[r][k]);
    }
    swap (b[z], b[r]);
}


const double eps = 1e-9; // cisla v absolutni hodnote mensi nez 10^9 povazujeme za nulu

int main()
{
    tisk ();
    int r = 0;
    int s = 0;
    while (r < N && s < N)
    {

       if (abs (a[r][s]) < eps)
       {
           int t = r+1;
           while (t < N && abs (a[t][s]) < eps)
           {
               t ++;
           }
           if (t < N)
               prehod (r, t);
       }

       if (abs (a[r][s]) >= eps) // pokud muzeme delit
       {
          deleni (r, a[r][s]); // a[r][s] upravime na jednicku
          for (int i=0; i