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Liebniz formula for determinant

Amer

Active member
Mar 1, 2012
275
Hey
libniz formula
i cant post picture and i cant use latex :(

if we want to use Libniz forumla for find the determinant of A such that

A = 1..-1..0..3
......2..-3..0..4
......0..2..-1..5
......1..2..2..3

sigma here from S_4 which has 4! elements which element will we choose
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,493
We must exclude permutations which map 1 to 3 or 2 to 3 or 3 to 1. Suppose 1 is mapped to 1. Then 2 is mapped to 2 or 4. Therefore, the permutations that start with 1 are (1, 2, 3, 4), (1, 2, 4, 3), (1, 4, 2, 3) and (1, 4, 3, 2). Now try to come up with the remaining 6 permutations.