Eigenvalues of a matrix

[login2]

Hello,
I have some hard times finding the eigenvectors of a specific matrix and I would be very happy if someone could help me with my question.
The matrix is:

1	0	0
0	1	-1
0	1	1

I have found the three eigenvalues:
λ₁ = 1, λ₂ = 1+i, λ₃ = 1-i

And for the eigenvectors I am able to find:
for λ₁ (0,0,0)^T , for λ₂(0,i,1)^T and for λ₃(0,-i,1)^T

As I said, I would be very happy if someone can tell me if I am making a mistake somewhere or explain me the way to find the eigenvectors.
Thanks in advance!

 

[Steven G]

Hello,
I have some hard times finding the eigenvectors of a specific matrix and I would be very happy if someone could help me with my question.
The matrix is:

1	0	0
0	1	-1
0	1	1

I have found the three eigenvalues:
λ₁ = 1, λ₂ = 1+i, λ₃ = 1-i

And for the eigenvectors I am able to find:
for λ₁ (0,0,0)^T , forλ₂(0,i,1)^T and forλ₃(0,-i,1)^T

As I said, I would be very happy if someone can tell me if I am making a mistake somewhere or explain me the way to find the eigenvectors.
Thanks in advance!

You should be able to check to see if your eigenvectors are correct. Please test that and if your wrong then we will help. (I think getting you to test your answers is being very helpful)