# characteristic polynomial

• November 20th 2010, 09:08 AM
nerdo
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.

Thanks
• November 20th 2010, 10:03 AM
HallsofIvy
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?
• November 20th 2010, 10:08 AM
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
• November 20th 2010, 10:25 AM
nerdo
Quote:

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
• November 20th 2010, 10:45 AM
1234567
Quote:

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.