I have a three by three diagnol matrix

[1,2,-4;0,2,1;0,0,3]

1,2,3

i found the eigenvectors for 2 and 3 but i am having finding the eigenvector for when lambda equals 1.

When I try to solve I can only find the vector x=0 which it cannot be.

I realize that this would be a problem with any diagonal matrix and was wondering how to go about finding the eigenvector.