Update: I mis-read the question. The question asks for a single computer setup, while I thought it was a two computer sync video setup.
I achieved exactly this using a 3x3 matrix of 9 computers using a mix of VLC & ssh. See What to do with a cluster of old computers running Ubuntu? for a pic.
I first tried doing the exact same thing that the other users suggested, but soon found out that running videos on sync is indeed a very difficult thing. I tried using crontabs to start videos at exactly the same time (after synchronizing clocks), but even if the command is issued at the same time, the player load times vary across computers, rendering it useless.
So the final solution I came up with was to stream the video using RTSP in VLC over a networked computer (which acts like the admin). I setup password-less ssh from admin to the two clients. And then finally, sent the commands over ssh to play the video.
VLC offers a special wall mode where you can break your video into a wall. Using that, you can specify any particular frame from the wall to be started in full-screen. So in my case, all 9 screens full-screened different portions.
I'll try to post the exact commands as soon as I can get them for you.
PS: A few recommendations :
* VLC does not stream everything perfectly. I found that streaming mpg files was easiest.
* Match the aspect ratio of the video with your monitors. (For instance if they're old CRTs (as in my case) with 4:3 ratio, then your video should probably be 8:3.