// Written by Hosung Leo Kim

#include <iostream>

using namespace std;


void dumpCoeff( float coeff[10][11], int N )
{
  for ( int i = 0; i < N; i++ )
  {
    for ( int j = 0; j < ( N + 1 ); j++ )
    {
      cout.setf( ios::fixed );
      cout.setf( ios::showpoint );
      cout.precision( 2 );
      cout.width(8);
      cout << coeff[i][j] ;
    }
    cout << endl;
  }
} // dumpCoeff()



int main()
{
  float coeff[10][11];
  
  int N = 3;
  
  coeff[0][0] =  2;
  coeff[0][1] =  3;
  coeff[0][2] =  1;
  coeff[0][3] = 11;
  
  coeff[1][0] =  4;
  coeff[1][1] = -2;
  coeff[1][2] =  3;
  coeff[1][3] =  9;
  
  coeff[2][0] =  3;
  coeff[2][1] =  5;
  coeff[2][2] = -3;
  coeff[2][3] =  4;
  
  
  dumpCoeff( coeff, N );
  
  for ( int i = 0; i < N; i++ ) // for each column
  {
    cout << endl << "column " << i << ":" << endl;
  
    float divisor = coeff[i][i];
  
    for ( int k = 0; k < ( N + 1 ); k++ )
      coeff[i][k] /= divisor;
  
    dumpCoeff( coeff, N );

    for ( int j = 0; j < N; j++ ) // for each row
    {
      if ( j != i )
      { 
        float multiplier = coeff[j][i];
  
        for ( int k = 0; k < ( N + 1 ); k++ )
          coeff[j][k] -= coeff[i][k] * multiplier;
   
        cout << endl;
        dumpCoeff( coeff, N );
      }
    } // for j
  } // for i
  
  
  return 0;
}

/*
/homes/home30/hkim16/107/lab10> a.out
    2.00    3.00    1.00   11.00
    4.00   -2.00    3.00    9.00
    3.00    5.00   -3.00    4.00

column 0:
    1.00    1.50    0.50    5.50
    4.00   -2.00    3.00    9.00
    3.00    5.00   -3.00    4.00

    1.00    1.50    0.50    5.50
    0.00   -8.00    1.00  -13.00
    3.00    5.00   -3.00    4.00

    1.00    1.50    0.50    5.50
    0.00   -8.00    1.00  -13.00
    0.00    0.50   -4.50  -12.50

column 1:
    1.00    1.50    0.50    5.50
   -0.00    1.00   -0.12    1.62
    0.00    0.50   -4.50  -12.50

    1.00    0.00    0.69    3.06
   -0.00    1.00   -0.12    1.62
    0.00    0.50   -4.50  -12.50

    1.00    0.00    0.69    3.06
   -0.00    1.00   -0.12    1.62
    0.00    0.00   -4.44  -13.31

column 2:
    1.00    0.00    0.69    3.06
   -0.00    1.00   -0.12    1.62
   -0.00   -0.00    1.00    3.00

    1.00    0.00    0.00    1.00
   -0.00    1.00   -0.12    1.62
   -0.00   -0.00    1.00    3.00

    1.00    0.00    0.00    1.00
   -0.00    1.00    0.00    2.00
   -0.00   -0.00    1.00    3.00
/homes/home30/hkim16/107/lab10>
*/