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Math Help - Singular Matrix Proof

  1. #1
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    Singular Matrix Proof

    Prove that an nxn matrix of:
    [1 2 3 .... n
    n+1 n+2 n+3 .... 2n
    2n+1 2n+2....3n
    ....
    (n-1)(n+1)....n^2]
    will always be singular.

    (Sorry, I don't know how to use the math HTML, but basically saying a matrix like
    [1 2 3 4
    5 6 7 8
    9 10 11 12
    13 14 15 16])
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tommiegirl13 View Post
    Prove that an nxn matrix of:
    [1 2 3 .... n
    n+1 n+2 n+3 .... 2n
    2n+1 2n+2....3n
    ....
    (n-1)(n+1)....n^2]
    will always be singular.

    (Sorry, I don't know how to use the math HTML, but basically saying a matrix like
    [1 2 3 4
    5 6 7 8
    9 10 11 12
    13 14 15 16])
    I haven't worked out the details, but this seems to cry out for an induction proof.

    -Dan
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Using the elemental operations C_1-C_2 and C_2-C_3 we obtain two equal columns.


    Fernando Revilla
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