# Finding a value in a matrix with distinct eigenvalues

• November 28th 2009, 12:56 PM
chewitard
Finding a value in a matrix with distinct eigenvalues
The matrix $A=\left(\begin{array}{ccc}-1&1&0\\-6&6&1\\k&0&0\end{array}\right)$

has three distinct real eigenvalues if and only if $x. Find $x$ and $y$.
• November 28th 2009, 01:16 PM
tonio
Quote:

Originally Posted by chewitard
The matrix $A=\left(\begin{array}{ccc}-1&1&0\\-6&6&1\\k&0&0\end{array}\right)$

has three distinct real eigenvalues if and only if $x. Find $x$ and $y$.

1) Calculate the characteristic polynomial of A ;

2) A polynomial $f(x)$ has a multiple root $\alpha$ iff $f(\alpha)=f'(\alpha)=0$ ;

3) Using the above check what could be be the possible multiple roots of the char. pol. of A and what have to be the values of k that'd allow such a thing to happen.

Tonio