# Thread: Eugen Values for matrix

1. ## Eugen Values for matrix

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?

2. 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.

3. But how did you get the 6 and 4?

4. hmm
So i get the determinant:
(1 - A)(5 - A) - (1)(1)

but how do i get to the next step?
A^2 - 6A + 4

5. Originally Posted by taurus
hmm
So i get the determinant:
(1 - A)(5 - A) - (1)(1)

but how do i get to the next step?
A^2 - 6A + 4
Common algebra. Expand the bracket and simplify.

CB

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# how can we found Eugen values

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