Suppose that the trace of a 2×2 matrix A is tr(A)=3, and the determinant is det(A)=−40. Find the eigenvalues of A

Question

ganeshie8 · Answer

I think you need to solve below :

$\large \lambda^2 -  \lambda (\text{trace} ) +   \text{determinant} = 0 $

anonymous · Answer

$$
\begin{bmatrix}
a&b\
c&d
\end{bmatrix}
$$

anonymous · Answer

$$
(a-\lambda)(d-\lambda)-bc=0
$$We know $ad-bc = -40$ and $a+d=3$.

anonymous · Answer

Make that $\lambda_1$ and $\lambda_2$.

anonymous · Answer

$$
ad-(a+d)\lambda+\lambda^2-bc = 0
$$Then we get: $$
\lambda^2-(\color{red}{a+d})\lambda +(\color{blue}{ad-bc})=0
$$So looking at that, I agree with @ganeshie8

anonymous · Answer

Thank you! I got my small eigenvalue and large eigenvalues mixed up. small eigen.= -5, and large eigen. = 8