I'm including a library which I know exists at the location I pointed to, but gcc is saying it cannot find it
I hope you are doing well.
MCUXpresso requires that you link the library’s path to the project properties. Here you will find a quick guide on how to do so: https://community.nxp.com/thread/388991
I hope this information helps. Do not hesitate to ask about any doubt or concern you have about your application.
Could you share the full commandline passed to the linker (you can copy it from the Console view)?
Your screenshot tells that it cannot find -l......, so it seems you have added a -l option with a file somehow, and it thinks it is a normal object file somehow. As for adding libraries: see Creating and using Libraries with ARM gcc and Eclipse | MCU on Eclipse where you can add the -l option with the search path. Another consideration (which seems not to be the case in your case: if you have spaces in the path, you need to put the path into double quotes).
I hope this helps,
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