Suppose that A is a 6 6 matrix with characteristic polynomial cA() = (1 + )

Question:

Suppose that A is a 6 × 6 matrix with characteristic polynomial cA(λ) = (1 + λ) (1 - λ)2 (2 - λ)3.
a. Prove that it is not possible to find three linearly independent vectors v1, v2, v3 in R6 such that Av1 = v1, Av2 = v2, and Av3 = v3.
b. If A is diagonalizable, what are the dimensions of the eigenspaces E-1, E1, and E2?