# Math Help - Determinants (using elementary row operations)

1. ## Determinants (using elementary row operations)

Hi, if anyone could explain how you get from
(x+y+z+t)det 1 1 1 1
qqqqqqqqqqq y z t x
qqqqqqqqqqq z t x y
qqqqqqqqqqq t x y z

to
(x+y+z+t)det 0 1 1 1
qqqqqqqqqq (y-z+t-x) z t x
qqqqqqqqqq (z-t+x-y) t x y
qqqqqqqqqq (t-x+y-z) x y z
that would be brilliant! Totally confused
PS. The qs are just in there to make the matrices slightly more lined up (spaces don't seem to work)! Ignore the qs

2. ## Re: Determinants (using elementary row operations)

I figured that step out but I am stuck again :/
The original question was: find
det x y z t
---- y z t x
---- z t x y
---- t x y z
as a product of linear factors

We end up with
(x+y+z+t)(x-y+z-t)det (t-y-z+x) 2(x-z)
----------------------- (y-t) --- (y+z-t-x)
Which is easy enough to solve I thought...
BUT, they give the final answer as -(x+y+z+t)(x+iy-z-it)(x-y+z-t)(x-iy-z+it)