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  3. let a =   [  0 2 0 1 0 2 0 1 0 ]

Let A =   [  0 2 0 1 0 2 0 1 0 ]  . (a) Find the...

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Advance Math

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.

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