Hi just wondering if anybody could help me with a problem i've can't see to solve!

I can work out the Eigenvalues fine

Matrix A = [ 2 -1

-1 1 ]

Ax = Lx L = lamda

| [A-LI] | = 0

(2-L)(1-L) - 1 = 0

L^2 - 3L + 1 = 0

L(1) = 0.38

L(2) = 2.62

Now this is where i run into trouble. i try solve the simulataenous equations from this, these are.

1. 1.62x1 - x2 = 0

2. 0.62x2 - x1 = 0

What do i do now, i've tried solving these but all i end up with is Cx1 = 0, which doesn't help anything, any help on what to do?