Converting example using yield and the iterator approach to a basic loop or using LINQ.

flattenMatrix().cs

// Your current code
 public static IEnumerable<T> Flatten<T>(this T[,] matrix)
    {
        var rows = matrix.GetLength(0);
        var cols = matrix.GetLength(1);
        for (var i = 0; i < rows;i++ )
        {
            for (var j = 0; j < cols; j++ )
                yield return matrix[i, j];
        }
    }

// Without yield, using LINQ
// @see http://de.wikipedia.org/wiki/LINQ
  int[,] array2d = ...;
  var array1d = array2d.Cast<int>().ToArray();

// Without yield, general solution
  int[,] array2d = ...;
  var rows = array2d.GetLength(0);
  var cols = array2d.GetLength(1);
  var array1d = new int[rows * cols];
  var current = 0;
  for (int i = 0; i < rows; i++)
  {
      for (int j = 0; j < cols; j++)
      {
          array1d[current++] = array2d[i, j];
      }
  }
  
// Without yield, shortest solution
  int[,] array2d = ...;
  var array1d = new int[array2d.GetLength(0) * array2d.GetLength(1)];
  var current = 0;
  foreach (var value in array2d)
  {
      array1d[current++] = value;
  }
  
// Usage:
 int[,] array2D = new int[,] { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };  
 int[] array1D = array2D.Flatten().ToArray();