Dual PC monitors plus TV Clone help..

I have a ATI 4800 Series video card with two DVI outputs.. Been using a dual display and now I want to clone one screen to my Samsung TV.. After doing a lot of research seems like DVI splitters don't work and powered DVI splitters are pricey.. Can someone tell me if this would work?

1. Off the video card connect one DVI port using a (DVi to HDMI Adapter) to the input of a (Powered HDMI Splitter)..

2. With two hdmi outputs off the (Powered HDMI Splitter) hook one to tv and the other to my pc monitor with another (DVi to HDMI Adapter)..

thanks