Issuing multiple commands through SSH

Simple newbie question:

I want to use SSH to login to a remote machine, make a backup of a file, gzip it and then logout using a simple bash script. I know I need to manually login but from then on I would like to execute the other commands automatically.

Here is the simplified code....

1 ssh admin@xxx.xxx.xx.xxx
2 cp file1 file1.bak
3 gzip file1.bak
4 exit

If I put this in a bash script I just get to the remote machine prompt. How can I get the remote machine to execute lines 2,3 and 4


Regards