OpenSUSE :: SSH Script - Make Changes To Several Computers At Once In A Private Network

I'm trying to make changes to several computers at once in a private network. I have ssh keys setup so that I can ssh from the main computer to all the other computers without having to enter my password. So I wrote a bash script like for computers in `cat computer list` do ssh $computers #type changes here exit done

but instead of executing the commands on every computer, it opens a shell on every computer for me to type into, just as if I had used ssh myself and not in a script. how to get this to work? I want to be able to add lines at the comment like "echo "test" > /testFile.txt" and be able to see the changes on each machine, in this case see testFile.txt on every machine.