Determinants and Cramer's Rule

[rocomath]

I'm trying to learn about Determinants and Cramer's Rule.

If a multiple of one row is added to another row, the value of the determinant is not changed. This applies to columns, also.

15 14 16
18 17 32
21 20 42

Factoring a 3 from C1 and a 2 from C3 =

6 times

5 14 13
6 17 13
7 20 21

Now subtracting C3 from C2 =

6 times

5 1 13
6 1 16
7 -1 21

So, C3-C2. Why isn't C2 ...

13-14 = -1
16-17 = -1
21-20 = 1

I notice it's just opposite signs, but where does the -1 multiple come from.

 

[rocomath]

Uh! Ok it says "subtract the third column from the second column" meaning C2-C3.