# Characteristic Polynomial

• April 21st 2010, 01:49 PM
dwsmith
Characteristic Polynomial
Let A be 2x2 and let $p(\lambda)=\lambda^2+b\lambda+c$ be the characteristic polynomial of A. Show that $b=-tr(A)$ and $c=det(A)$.

I know with a 2x2 matrix that $\lambda^2-tr(A)\lambda+det(A)$ forms the characteristic polynomial; however, I am not sure on how to prove it. I am guessing it is probably trivial if I know that.
• April 21st 2010, 02:23 PM
pickslides
• April 21st 2010, 02:31 PM
dwsmith
I know what the website is saying. The problem is in making it coherent and mathematical correct in the proof.
• April 21st 2010, 02:40 PM
pickslides
Let $A = \left(\begin{array}{cc}a&b\\c&d\end{array}\right)$

Then find the charateristic polynomial

$p(\lambda) = \left|\begin{array}{cc}a-\lambda &b\\c&d-\lambda1\end{array}\right|$

Then find the trace and the deteminant. The rest is up to you (Rofl)