Is there an eigenvector of A or no?

Question

Is v=[-1 an eigenvector of A=[ 2 -2 ?

1] -4 0]

If so, find the eigenvalue?

Answer 1

|[2-λ -2]|

|[-4 -λ]| = λ²-2λ-8

λ = 4, -2

For λ=4

[-2 -4]

[-2 -4]

~

[1 1]

[0 0]

[1 1][v₁] [0]

[0 0][v₂] = [0]

v₁ = -v₂

let v₂ = 1 --> v₁ = -1

So v = [-1 1]^t

The answer is yes for eigenvalue = 4