- #1
jrcdude
- 16
- 0
Homework Statement
Show that the descriminant of the characteristic polynomial of K is greater than 0.
[tex]K=\begin{pmatrix}-k_{01}-k_{21} & k_{12}\\
k_{21} & -k_{12}
\end{pmatrix}
[/tex]
And [itex]k_i > 0[/itex]
Homework Equations
[tex]b^2-4ac>0[/tex]
The Attempt at a Solution
I have tried the following:
[tex]
\begin{pmatrix}-k_{01}-k_{21}-\lambda & k_{12}\\
k_{21} & -k_{12}-\lambda
\end{pmatrix}
[/tex]
Bringing me to
[tex]\lambda^{2}+(k_{12}+k_{01}+k_{21})\lambda+k_{01}k_{12}=0[/tex]
And then plugging it into discriminant form
[tex](k_{12}+k_{01}+k_{21})^{2}-4(k_{01}k_{12})>0[/tex]
But from there I don't think that is a true statement.
Any help would be appreciated, thanks.