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Find all values of c ∈ C such that the linear transformation T ∈ L(C3) given...

Find all values of c ∈ C such that the linear transformation T ∈ L(C3) given by T(z1, z2, z3) = (z1 + 2z2 + 2z3, −z2 + cz3, z3) is diagonalizable. For those values of c, find a basis of C3
such that the matrix of T corresponding to that basis is diagonal.

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