I have a three by three diagnol matrix

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

$\displaystyle \lambda=$ 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 $\displaystyle (A-\lambda I)x=0$ 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.