Find the general solution of the given system.
The given matrix is X' = (1st row (1,-1,2) 2nd row (-1,1,0) 3rd row (-1,0,1))X
2. The attempt at a solution
The eigenvalue determinant = (1st row (1-λ,-1,2) second row (-1,1-λ,0) 3rd row (-1,0,1-λ)
Solving the determinant gives -(λ-1)(λ^2-2λ+2)
So λ1,2 = 1+i and 1-i and λ3 = 1
Now my question is how do I solve the 3x3 matrix with copmlex numbers in it? I used gaussian elimination to solve for the real value λ3.
(1st row (-i,-1,2) 2nd row (-1,-i,0) 3rd row (-1,0,-i)) multiplied by the column (k1,k2,k3) = 0