I have the following 2x2 matrix:
(1-A) 1
1 (5-A)
I need to solve to get the Eigen values. How do i develop the quadratic eqn from that to solve for A?
If I understand correctly, we have the matrix $\displaystyle A=\begin{bmatrix}1&1\\1&5\end{bmatrix}$
we can find the eigenvalues by $\displaystyle \begin{bmatrix}1-{\lambda}&1\\1&5-{\lambda}\end{bmatrix}$
The characteristic polynomial is given by $\displaystyle Det({\lambda}I-A)$
$\displaystyle Det\left({\lambda}\cdot\begin{bmatrix}1&0\\0&1\end {bmatrix}-\begin{bmatrix}1&1\\1&5\end{bmatrix}\right)$
$\displaystyle ={\lambda}^{2}-6{\lambda}+4$
Solve the quadratic to find the eigenvalues.