Adding Rows To data grid View in WPF 4.0 in already created column

<Window x:Class="WpfApplicationTest.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
    <Grid>
        <DataGrid ItemsSource="{Binding Path=DataView}"/>
    </Grid>
</Window>

public partial class MainWindow : Window
{
        private DataTable DataTable { get; set; }
        public DataView DataView { get; set; }

        public MainWindow()
        {
            InitializeComponent();

            DataTable = new DataTable();
            DataTable.Columns.Add("Test");

            DataView = DataTable.DefaultView;
            DataContext = this;
            
            AddRow();
            AddRow();
        }

        private void AddRow()
        {
            DataRow dr = DataTable.NewRow();
            dr["Test"] = "Wert1";
            DataTable.Rows.Add(dr);
        }
      
}