How does SUMPRODUCT() work for Multiple Criteria Aggregations?

I most often need to SUM or COUNT rows in a table that meet a set of criteria. The formulae that can be used to accomplish this task include:

SUMIFS(), COUNTIFS(), SUMPRODUCT()

I prefer SUMPRODUCT() because it is much more intuitive.

Here's an example of a simple Structured Table:
[pre]
Table: tSample
Date Name Amt
2/1/2017 Al 22
2/13/2017 Al 33
2/25/2017 Al 23
2/5/2017 Bob 32
2/21/2017 Bob 21
3/9/2017 Bob 12
2/6/2017 Fred 42
2/22/2017 Fred 24
3/3/2017 Al 24
3/17/2017 Bob 14
[/pre]

Here's a summary table:
[pre]
Name 29-Jan [color #204A87]12-Feb[/color] [color #CE5C00]26-Feb[/color] 12-Mar 26-Mar
[color #A40000]Al[/color] 22 [highlight]56[/highlight] 24 0
Bob 32 21 12 14
Fred 42 24 0 0
[/pre]

This is the formula [highlight]here[/highlight]:
=SUMPRODUCT([color #204A87](tSample[Date]>=C$1)[/color]*[color #CE5C00](tSample[Date]<D$1)[/color]*[color #A40000](tSample[Name]=$A2)[/color]*(tSample[Amt]))

Here's how this works:
[pre]
Table: tSample 12-Feb 26-Feb SUM=56
Date Name Amt [color #204A87](tSample[Date]>=F$1)[/color] * [color #CE5C00](tSample[Date]<G$1)[/color] * [color #A40000](tSample[Name]=$E2)[/color] * (tSample[Amt])
2/1/2017 Al 22 Al FALSE * TRUE * TRUE * 22 = 0
2/13/2017 Al 33 Al TRUE * TRUE * TRUE * 33 = 33
2/25/2017 Al 23 Al TRUE * TRUE * TRUE * 23 = 23
2/5/2017 Bob 32 FALSE * TRUE * FALSE * 32 = 0
2/21/2017 Bob 21 TRUE * TRUE * FALSE * 21 = 0
3/9/2017 Bob 12 TRUE * FALSE * FALSE * 12 = 0
2/6/2017 Fred 42 FALSE * TRUE * FALSE * 42 = 0
2/22/2017 Fred 24 TRUE * TRUE * FALSE * 24 = 0
3/3/2017 Al 24 Al TRUE * FALSE * TRUE * 24 = 0
3/17/2017 Bob 14 TRUE * FALSE * FALSE * 14 = 0
[/pre]

So any row where there are all TRUE , the PRODUCT calculates. Otherwise ZERO. Then you get the SUM of the PRODUCTS. If you were to eliminate the (tSample[Amt]) in the SUMPRODUCT, you'll get a COUNT of the rows that meet all the criteria.