Why is a negative sign not needed when swapping rows in matrix row echelon form?

[rapids79]

Hi..I have a very basic query...while solving a determinant, when we exchange/swap 2 rows we need to add a negative sign to the determinant. However, when we are trying to reduce a matrix to a row echelon form, when we swap 2 rows..do we need to add a negatice sign here as well? Well..from what I've read...theres no need to..But I'm not sure why..can anyone throw some more light on this??..thanks

 

[HallsofIvy]

You are confusing two completely different things.

When you "row reduce" to find a determinant, you want to keep the result the same- the determinant.

When you row reduce to row-echelon form, you are getting a completely new matrix- you don't have to do anything to "keep them the same" because they aren't supposed to be "the same".