What is this tube on my Matrix 2006

The only things that should have to be removed from stock air box and re connected to the cold air intake tube are the mass air flow sensor which is the sensor held on by two small screws on top of air box and a small hose that is connected to the bottom of the stock air box under the main intake tube behind the air box if your standing in front of car looking at engine. The hose your arrows are pointing at should not be hooked up to the air intake tube at all. Is it connected to something on both ends or is it just hanging there from the engine not connected to anything on the other end? I can't tell in the picture

Lol dude that's the vacuum hose trust me you'll want to put that back on after you're done doing what ever it is you're doing.. 99% of cold air systems come with a little nozzle connected to the main tube, that's where you connect the vacuum hose, or you can get a little tiny cone filter for the vacuum hose.