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?

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- Nov 8th 2009, 09:10 AMtaurusEugen 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, 09:45 AMgalactus
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. - Nov 8th 2009, 10:22 AMtaurus
But how did you get the 6 and 4?

- Nov 8th 2009, 07:39 PMtaurus
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, 08:33 PMCaptainBlack