Okey, im trying to find the eigenvectors of a 3x3 matrix.

(I have found the eigenvalues)

I'm going to use an example so I can solve my own matrix myself;

In this example the eigenvectors are found, but how?

So my question isHow are the calculations done to recieve the values of x, y, and z (eigenvectors)?

Eg. take example 1 with the eigenvalue of 0

Any help appriciated!