The term "Non-dependent EIC" can only refer to the situation where divorced parents have an agreement and the custodial parent "allows" the non-custodial parent to claim the child as their dependent. (It's a little more complicated, but that's the idea)
When this happens, the non-custodial parent still can't use the child for certain credits, and the Earned Income Credit is one of them.
In this situation, the custodial parent, although not claiming the child as their dependent, does get the EIC based on the child even though the child is not being claimed as their dependent, thus the "Non-dependent EIC"
In your situation, you would need to claim Person A as your dependent to have it impact your EIC.
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