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Math Help - Determinant Question

  1. #1
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    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
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  2. #2
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    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.
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  3. #3
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    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.
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