How do i convert mkv (HD video) files to HD avi or mp4 files so my ps3 will play them?

I have recently downloaded a few movies in hd, and they look very good, but i find my laptop screen a bit to small compared to the 46inch tv in the living room.. So i'd like to get my movies onto the tv somehow, without losing its quality. I have downloaded a program called OJ-soft total video converter, and converted the movie to a 1280x720 AVI, but the file seems way too small with its 560MB (compared to the 1.09GB original) and nothing plays it. i've tried other computers dvd players ps3 etc and nothing will play it.. so does anyone know any ways to make my ps3 and therefore my tv play these mkv files?