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Math Help - Matrix to Quadratic equation Help

  1. #1
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    Matrix to Quadratic equation Help

    Hi all, this is my first post

    Could somebody point in the right direction for solving this question.

    I have a 2X2 matrix A
    -50 -8
    336 54
    i am asked to find in terms of m, the expression det(A-mI)
    and show it as a quadratic expression
    [IMG]file:///C:/Users/IANDUG%7E1/AppData/Local/Temp/moz-screenshot.png[/IMG]
    Where do i start? I am probably missing something really obvious


    All help appreciated

    Ian999
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Ian999 View Post
    Hi all, this is my first post

    Could somebody point in the right direction for solving this question.

    I have a 2X2 matrix A
    -50 -8
    336 54
    i am asked to find in terms of m, the expression det(A-mI)
    and show it as a quadratic expression
    [IMG]file:///C:/Users/IANDUG%7E1/AppData/Local/Temp/moz-screenshot.png[/IMG]
    Where do i start? I am probably missing something really obvious


    All help appreciated

    Ian999
    What is mI?
    \displaystyle m \left [ \begin{array}{11} 1 & 0 \\ 0 & 1 \end{array} \right ] = \left [ \begin{array}{11} m & 0 \\ 0 & m \end{array} \right ]

    So what would be the matrix A - mI? Now take the determinant.

    -Dan
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  3. #3
    MHF Contributor

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    Assuming your matrix is \begin{bmatrix}-50 & -8 \\ 336 & 54 \end{bmatrix}

    Then "det(A- mI)" is the determinant
    \left|\begin{array}{cc}-50- m & -8 \\ 336 & 54- m \end{array}\right|

    Calculate that determinant.
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  4. #4
    Newbie
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    Feb 2011
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    Thanks

    Thanks for the advice guys.
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