Final answer:
Archie's filing status would be 'Single' as his wife passed away two years ago, and he cannot claim the 'Head of Household' status despite having a dependent child.
Step-by-step explanation:
Archie's filing status would be 'Single' as his wife passed away two years ago. Filing status refers to the category that determines the tax rates and deductions a taxpayer is eligible for on their income tax return. In this case, Archie does not have a spouse, so he would file as a single individual.
Having a dependent child would qualify Archie for the 'Head of Household' filing status, which offers more favorable tax rates and deductions compared to filing as 'Single.' However, since Archie's wife passed away and he is not legally considered a widow or widower, he cannot claim the 'Head of Household' status.
Therefore, Archie's filing status would be 'Single'.