# Thread: characteristic polynomial

1. ## characteristic polynomial

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

$3 \times 3~matrix$

$$\left( \begin{array}{ccc} 2 & 1 & 0 \\ 0 & 3 & 0 \\ 1 & 0 & 0\end{array} \right)$
$

is given by the formula
$$\chi(\lambda) = \left| \begin{array}{ccc} \lambda - 2 & -1 & 0 \\ 0 & \lambda - 3 & 0 \\ -1 & 0 & \lambda \end{array} \right|.$
$

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

2. 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?

3. 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

4. Originally Posted by nerdo
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

5. Originally Posted by nerdo
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.