# Determinant Question

• March 11th 2008, 02:06 PM
Jim Newt
Determinant Question
Find det D if

det D = 0 ... 0 0 0 d1
0 ... 0 0 d2 0
0 ... 0 d3 0 0
. . . . . .
. . . . . .
. . . . . .
dn ... 0 0 0 0

Any suggestions and/or strategies on this problem? Thanks greatly,

Jim
• March 11th 2008, 02:10 PM
Jim Newt
Boy that determinant doesn't look right when I posted it (looked different in the preview). Here's how its supposed to look:

Everything under the "Det=" row needs to be shifted to the right 4 or 5 spaces. For instance the first column top to bottom would read: 0, 0, 0, ... dn.
• March 11th 2008, 02:15 PM
ThePerfectHacker
The determinant of a diagnol matrix is the product of its entries in diagnol. This is not a diagnol matrix but you can make it into a diagnol matrix by moving the lower row to the top and the upper row to the bottom. Whenever you make this switch you get a -1 factor. In total you make $[n/2]$ switches (where [ ] is greatest integer function). Thus you get $(-1)^{[n/2]}d_1...d_n$ as the determinant.