Google Sheets ArrayFormula with Sumifs
The solution that I ended up using was this:
Credit due to 2n9 from google forums. Here is the link
=arrayformula(sumif(B3:B8&C3:C8,F3:F8&"A",A3:A8))
There were some other very good answers there using queries from Jean-Pierre Verhulst:
=query(A2:C8, "select B, sum(A) group by B pivot C")
=query(query(A2:C8, "select B, sum(A) group by B pivot C"), "select Col2, Col3")
=ArrayFormula(query(query(A2:C8, "select B, sum(A) group by B pivot C"), "select Col2, Col3 offset 1",0)+0)
Each of these solutions solves the problem but in a different way. They have different attributes such as removing headers or choosing only a certain column. Use the link to the google forum for more information.
Hope this helps someone.