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Math Help - Indefinite matrix

  1. #1
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    Indefinite matrix

    hello to everybody !

    could someone shed a light on this please.

    the following matrix is given:

    Code:
    2, 5, 1, 0
    5, 2, -2, 1
    1, -2, 1, 0
    0, 1, 0, 8
    now, show that this matrix is indefinite by calculating (x^t)(Ax) with the vektors x^t = (1,1,0,0) and x^t=(0,1,1,0).
    thanks in advance!
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  2. #2
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    Quote Originally Posted by vanilla1 View Post
    hello to everybody !

    could someone shed a light on this please.

    the following matrix is given:

    Code:
    2, 5, 1, 0
    5, 2, -2, 1
    1, -2, 1, 0
    0, 1, 0, 8
    now, show that this matrix is indefinite by calculating (x^t)(Ax) with the vektors x^t = (1,1,0,0) and x^t=(0,1,1,0).
    thanks in advance!
    For example:

    x^tAx=(1\;1\;0\;0)\begin{pmatrix}2&5&1&0\\5&2&\!\!  \!\!-2&1\\1&\!\!\!\!-2&1&0\\0&1&0&8\end{pmatrix}\left(\begin{array}{c}1  \\1\\0\\0\\\end{array}\right) =14>0 .

    Now show that with the other vector you get a negative result and thus A is indefinite.

    Tonio
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  3. #3
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    Tonio, thank you very much!
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