Each equation (or line of the matrix) turns out to be just zero. The determinant of a zero matrix is zero.
Im normally ok with these sort of questions but this one has me stumped!
I need to show using row operations that the following determinant = 0
| (y-z) (z-x) (x-y) |
| (z-x) (x-y) (y-z) | = 0
| (x-y) (y-z) (z-x) |
I tried doing it the usual way as you would if the matrix contained number instead of variables, but it ended up becoming very messy and I couldnt help but think there was a better way of doing it.
the horizontal lines :
are supposed be the determinant notation.
Thanks in advance.