I am having to learn how to do jacobian matrices, determinants, and finding eigenvalues on my own and I cannot seem to find reasonable eigenvalues for this jacobian matrix.
When I try to solve it I get absurdly long answers. My professor mentioned the Routh Hurwitz method but I after attempting to learn it on wikipedia and youtube It was just over my head at the level I am right now. If you could point me in the right direction that would be greatly appreciated, an explanation is more helpful to me in the long run than just an answer, since I have to do more jacobian matrices more complicated than this one.
$$
\begin{pmatrix}
-C_+ – \mu & 0 & -\beta T_+ \\
C_+ \beta & -\alpha & \beta T_+ \\
0 & k & -\gamma
\end{pmatrix}
$$
Thank you in advance, I truly appreciate anyone who takes the time to try and help me.
Best Answer
From our discussion in the comments, you are interested in solving $$\det\left(\left[\begin{array}\ (-C^+\beta-\mu-\lambda)&0&-\beta T_+ \\C^+\beta&-\alpha-\lambda&\beta T_+ \\0&\kappa&-\gamma-\lambda \end{array} \right] \right)$$