I've already found the eigen value of a matrix,and substituted for the value of lambda,this is the resulting matrix

0 1 0 0
0 0 1 0
0 0 0 0

the unknows are x y z in that order,how do I find the eigen vectors if the last column is the solution matrix and what is the eigen value?

Thanks in advance :)

So if your original matrix is called A, and the eigenvalue is λ then A - λI =

[0 1 0]
[0 0 1]
[0 0 0].

I hope this is what you meant, because it is what I understood you to say. The equations associated with this are

y = 0
z = 0
0 = 0.

This means that y = z = 0, but x can be anything. All eigenvectors are of the form (x, 0, 0) where x is any nonzero number. A good representative is (1, 0, 0).