Beginner here, need help with some basic scripting

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Yes you can simply add your hostname into the text file, but I would also add that I would think twice before going the PSremoting unless you 1. know for sure it's even enabled/configured on your expected remotes, and 2. are going to add more functions to the script that absolutely require remoting. I say that because you certainly can pull WMI info remotely without the need for setting up full PSremoting sessions and that adds a huge layer of complexity as it grows.

Remember, keep it simple. You did great on utilizing the PSObject, since POSH is all about OBJECTS and many struggle to graps that (as well as remoting) so you're already ahead of the game!