This is a matrix of the homogeneous equation x'=Ax, and I want to find it's eigenvectors. here, I have defective eigenvalues with defect p and -p. I should find two linearly independent vectors which satisfy these equations: v0=(A+ lambda I)^2 =0, v1=(A+ lambda I) v0, I =denoting a 6*6 identity matrix, lambda = p or -p, and Power in the first equation is a rank generalized eigenvector associated with lambda. Could you please help to find substitutions that bring the rank 1, 3 , 4 of 2 if it is possible?

Thanks