**Unformatted text preview: **term is a product of one entry from each row and each column. In the description above, the
products are listed in order, 1st row, 2nd row, and then 3rd row. We don’t have to use this ordering, of
course, but when we do, the column numbers appear in every possible ordering. Now, some of the terms have
negative signs, which can be related to the ordering of the column numbers. In particular, even permutations
1 MA 3280 Lecture 19 - Determinants 2 of the numbers 1, 2, and 3 correspond to a plus sign, and odd permutations correspond to a negative sign.
So what is an odd or even permutation?
Even and odd permutations. Let’s start with the standard ordering of the numbers 1, 2, and 3, 123. One
way of changing the ordering of these numbers is to transpose two of them, like 132, where I’ve reversed
the 2 and 3. From here, I could do another transposition to get 312. Since it took two transpositions to
get from 123...

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