Let A = 0 2 0
1 0 2
0 1 0 .
(a) Find the eigenvalues of A and bases of the correspondingeigenspaces.
(b) Which of the eigenspaces is a line through the origin? Writedown two vectors parallel to this line.
(c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W, or explain why such a plain does not exist.
(d) Write down explicitly a diagonalizing matrix S, and adiagonal matrix Λ such that S −1AS = Λ; A = SΛS −1 . or explain whyA is not diagonalizable.
