Hey guys,

i am supposed to determine the eigenvalues and eigenvectors of:

$\displaystyle \begin{pmatrix}1 & 1 \\1 & 0\\ \end{pmatrix}$

I calculated the eigenvalues with the formula:

$\displaystyle det(\lambda I - A) = 0$

to be $\displaystyle \lambda_1 = \frac{1}{2}(1 + \sqrt 5)$ and $\displaystyle \lambda_2 = \frac{1}{2}(1 - \sqrt 5)$

To get the eigenvectors i need to solve the following equation, right?

$\displaystyle \begin{pmatrix}\lambda - 1 & -1 \\-1 & \lambda\\ \end{pmatrix}\cdot\begin{pmatrix}x \\ y \end{pmatrix} = \begin{pmatrix}0 \\ 0 \end{pmatrix}$

Now i get x = 0 and y = 0, but thats just not right says Wolfram Alpha and the exercise text.

What is wrong?

Thanks, Inf