quick tv input/ output/ surround sound question

i am trying to get the full potential from my 5.1 channel surround sound, which is currently only hooked up with av inputs for my ps3 and cable box. My tv has a coaxial output. Would this mean that the tv has, basically a built in receiver? What i want to do is hook up the ps3 through HDMI to the tv and the surround sound to the tv through coaxial (surround sound has coaxial in but no toslink or hdmi in).

Does anyone know if connecting the surround sound to the tv through this method would cause any audio being transmitted to the tv to be outputted to the surround sound and give me 5.1 channel surround sound?

Also, does anyone know what the coaxial output on the tv would be used for if it is not to transfer sounds to a surround sound system?

Thanks in advance.

Your TV cannot pass 5.1 HDMI audio to the coaxial output. At most, you will be getting stereo. Your receiver could upmix it to 5.1, but it would not be true surround sound.

My advice is to get a receiver with optical (toslink) inputs and hook the PS3 up to it directly.