Im am nearly there to find the corrosponding eigenvector.

I solved the equation (A - lambda * E)*x = 0, where x and 0 are vectors

and the result is

(0,1,0)

(0,0,1)

(0,0,0)

how do I find the corrosponding vector? Maple says (1,0,0), but how do I reach that conclusion?