title: Program to solve a system of linear equations in C++
body: <p>I am testing this code for solving linear systems with this simple 2-equation system (in matrix form "Mat[2][3]"), but when I execute it, I obtain the following result, which does not agree with the coefficients I have introduced in the system Matrix:</p>
  
  <p>CODE:</p>
  
  <pre><code>//Gauss Elimination
  #include &lt;iostream&gt;
  #include &lt;cmath&gt;
  #include &lt;vector&gt;
  #include &lt;fstream&gt;
  #include &lt;iterator&gt;
  #include &lt;string&gt;
  #include &lt;iomanip&gt;
  using namespace std;
  
  int main() {
  
      double Mat[2][3];
      vector&lt;double&gt; q(2);
      int Nx = 2, ii, jj, kk;
  
      Mat[1][1] = 2.0;
      Mat[1][2] = 3.0;
      Mat[1][3] = 2.5;
      Mat[2][1] = 1.3;
      Mat[2][2] = 3.0;
      Mat[2][3] = 2.5;         
  
      cout &lt;&lt; "Matrix: " &lt;&lt; endl;     
      for (ii = 0; ii &lt; Nx; ii++) {
          for (jj = 0; jj &lt; Nx + 1; jj++) {
              cout &lt;&lt; Mat[ii][jj] &lt;&lt; "   ";
              cout &lt;&lt; endl;
          }
      }
      // Triangularization
      for (ii = 0; ii &lt; Nx - 1; ii++)
          for (kk = ii + 1; kk &lt; Nx; kk++)
          {
              double t = Mat[kk][ii] / Mat[ii][ii];
              for (jj = 0; jj &lt;= Nx; jj++)
                  Mat[kk][jj] = Mat[kk][jj] - t * Mat[ii][jj];
          }   // Resolution
      for (ii = Nx - 1; ii &gt;= 0; ii--)
      {
          q[ii] = Mat[ii][Nx];
          for (jj = Nx - 1; jj &gt; ii; jj--)                        
              q[ii] = q[ii] - Mat[ii][jj] * q[jj];
          q[ii] = q[ii] / Mat[ii][ii];
      }
  
      cout &lt;&lt; "Solution of the system: " &lt;&lt; endl;
      cout &lt;&lt; q[1] &lt;&lt; endl;
      cout &lt;&lt; q[2] &lt;&lt; endl; ////////////////////////////////////////////////////////////////////////
  
  
      return 0;
  }
  </code></pre>
  
  <p>RESULT:</p>
  
  <pre><code>Matrix: 
  0   2.07496e-317   6.95314e-310   
  0   2   3   
  Solution of the system: 
  -nan
  0
  </code></pre>