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

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- Mar 11th 2008, 02:06 PMJim NewtDeterminant 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 - Mar 11th 2008, 02:10 PMJim 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. - Mar 11th 2008, 02:15 PMThePerfectHacker
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 switches (where [ ] is greatest integer function). Thus you get as the determinant.