[[ a_{11} a_{12} \cdots a_{1n} | b_1]
 [ 0  (a_{22} - \frac{a_{}_{21}}{a_{22}}a_{11}) \cdots a_{2n} | b_2 - \frac{a_{21}}{a_{11}}b_1 ]]

#+BEGIN_SRC c
  for (int i = 1; i < n; i++) {
    float factor = -a[i][0] / a[0][0];
    for (int j = 1; j < n; j++) {
      a[i][j] = a[i][j] + factor * a[0][j];
    }
    b[i] = b[i] + factor * b[0];
  }

  for (int k = 0; k < (n - 1); k++) {
    for (int i = k+1; i < n; i++) {
      float factor = -a[i][k] / a[k][k];
      for (int j = k+1; j < n; j++) {
        a[i][j] = a[i][j] + factor * a[j][k];
      }
      b[i] = b[i] + factor*b[k];
    }
  }
#+END_SRC