How do I tell if my graphics card can handle gnome 3?

view story

http://forums.fedoraforum.org – Gnome 3 requires hardware accleration. Gnome 3 worked fine but recently it keeps going into fallback mode. The reason given is that supposedly my graphics card can't handle gnome 3. It is possible that some recent change led to that, but I would like to determine just what the problem is. How do I determine, under Fedora 17, if my graphics card has hardware acceleration? If that is not it, what else might I do to troubleshoot the problem? System settings identifies my graphics as Gallium 0.4 on AMD RV620. My compuer is a Dell Precision 3500 purchased in January, 2011. The invoice (HowTos)