# Eugen Values for matrix

• Nov 8th 2009, 10:10 AM
taurus
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?
• Nov 8th 2009, 10:45 AM
galactus
If I understand correctly, we have the matrix $A=\begin{bmatrix}1&1\\1&5\end{bmatrix}$

we can find the eigenvalues by $\begin{bmatrix}1-{\lambda}&1\\1&5-{\lambda}\end{bmatrix}$

The characteristic polynomial is given by $Det({\lambda}I-A)$

$Det\left({\lambda}\cdot\begin{bmatrix}1&0\\0&1\end {bmatrix}-\begin{bmatrix}1&1\\1&5\end{bmatrix}\right)$

$={\lambda}^{2}-6{\lambda}+4$

Solve the quadratic to find the eigenvalues.
• Nov 8th 2009, 11:22 AM
taurus
But how did you get the 6 and 4?
• Nov 8th 2009, 08:39 PM
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
• Nov 8th 2009, 09:33 PM
CaptainBlack
Quote:

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