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No, you cannot claim the Earned Income Credit (EIC).
Your wife is considered a resident for tax purposes once she met the Substantial Presence Test in 2015 or 2016 (assuming she was never a full time student).
If you lived together then you are not able to file as head of household. You can only file a married filing jointly or married filling separately. But in both cases you would not qualify for EIC. Please see What are the qualifications for the Earned Income Credit (EIC or EITC)?
