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Math Help - characteristic polynomial

  1. #1
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    characteristic polynomial

    The \emph{characteristic polynomial} $\chi(\lambda)$ of the

    $3 \times 3$~matrix

    \[ \left( \begin{array}{ccc}<br />
2 & 1 & 0 \\<br />
0 & 3 & 0 \\<br />
1 & 0 & 0\end{array} \right)\] <br />




    is given by the formula
    \[ \chi(\lambda) = \left| \begin{array}{ccc}<br />
\lambda - 2 & -1 & 0 \\<br />
0 & \lambda - 3 & 0 \\<br />
-1 & 0 & \lambda \end{array} \right|.\] <br />


    Characteristic polynomial should be x^3-5*x^2+6*x but cannot make the metrix satisfy the equation.

    Can someone please help me.

    Thanks
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  2. #2
    MHF Contributor

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    Well, before we can help you we would need to know what you did! Did you expand this by the first row or first column? What did you get?
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  3. #3
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    Yh i just expanded it and it does satisfy the above Characteristic polynomial since A^3-5*A^2+6*A=0.

    Thanks for the help

    By The Way what will be an equivalent metrix to A
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  4. #4
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    Quote Originally Posted by nerdo View Post
    Yh i just expanded it and it does satisfy the above Characteristic polynomial since A^3-5*A^2+6*A=0.

    Thanks for the help

    By The Way what will be an equivalent metrix to A

    Way what will be an equivalent metrix to A
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  5. #5
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    Quote Originally Posted by nerdo View Post
    what will be an equivalent metrix to A
    Hint: Find a matrix that has the same Rank as A.

    To do this Find the Rank of A and another metrix which has the same Rank.
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