Let A be a real 3 × 3 matrix, u and v linearly independent vectors in R3 such that Au = u
and Av = v. Suppose w is a vector in R3 such that Aw = w + u + v.
(i) Find all eigenvalues of A.
(ii) Solve the differential system x′ = Ax.
For (ii) I know that 1 is definitely an eigenvalue, is there any other eigenvalues apart from 1? Thanks in advance!