Update database from datagridview with linq

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C#

LINQ

I'm trying to update my database from a datagridview, but although the code compiles, the changes aren't saved.

Basically:
1)bind datagridview to a query,
2)make changes to the data on the datagridview,
3)use cellendedit to capture change and update database.

Please take a look at the code below.

Sorry for such a simple question, but I've been trawling the net and haven't found a solution using Linq that works.

What I have tried:

private void grdBOOK_CellEndEdit(object sender, DataGridViewCellEventArgs e)
        {
            using (lnkTRADERDataContext DATActx = new lnkTRADERDataContext())
            {
                grdBOOK.EndEdit();
                DATActx.SubmitChanges();
            }
}