Let T: M3x3 (C) → M3x3 (C) be the linear operator over C defined by T (X) AX where 1 1 0 01 0 and let W be the T-cyclic subspace of M3x3 (C) generated by I3. 00 -1 A = (2.1) Find the T-cyclic basis for W generated by I3. (2.2) Find the characteristic polynomial of Tw. (2.3) Given that λ = 1 is an eigenvalue of Tw, find a corresponding eigenvector in W expressed as a linear combination of the T-cyclic basis for W.

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