Hallo,
Die Determinante lautet:
\( \left|\begin{array}{ccc}3 -\lambda & -2 & 0 \\ -2 & 2-\lambda & -2 \\ 0 & -2 & 1-\lambda\end{array}\right|=0 \)
Nach Laplace:
\( (3-\lambda)\left|\begin{array}{cc}2-\lambda & -2 \\ -2 & 1-\lambda\end{array}\right|+ \)
\( 2\left|\begin{array}{cc}-2 & -2 \\ 0 & 1-\lambda\end{array}\right|+0\left|\begin{array}{cc}-2 & 2-\lambda \\ 0 & -2\end{array}\right| \)
-------->
\( -\lambda^{3}+6 \lambda^{2}-3 \lambda-10=0 \)
λ1= -1
λ2= 2
λ3= 5
