I have matrix

and I get that

so

//after this our lecturer takes random numbers and checks if they can be eigenvalues.

For this problem I'm sure that eigenvalue is only

//but what if I get ?

//I have to check all numbers till 6

//so how did he find that for this one is and so fast?

//EH... NEVERMIND xD

further, to find eigenvector I have

but I can't find a way to substitute so that I would have 2 even rows or columns, so maybe there is another way I don't know?

some update:

I ended up at

So, after getting someone annoying for updating my post so many times xD

Q: HOW DO I STANDARDIZE EIGENVECTOR AND CHECK IF ANSWER IS CORRECT?

someone told me: "you need to find vector length or smth" =/

???????

IF CORRECT, HOW DO I CHECK IF IT IS SO?