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6. For the following linear operator T on a vector space V (equipped with usual addition and scalar multiplication operations), perform the following two tasks:

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6. For the following linear operator T on a vector space V (equipped with usual addition and scalar multiplication operations), perform the following two tasks: (i) Test whether T is diagonalizable (show your steps); (ii) Find a basis f for V such that , is a diagonal matrix. (a) V = P2(R), T(f) = f(0) + f(1)x + f(1)x2 (b) V = C2, T(z, W) = (z + iw, iz + w)

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