LetV be the complex inner product space3 with inner product given by the usual dot product, and letTL(V) be given byT(z1,z2,z3) = (z3, 2z2, -z1)

Let V be the complex inner product space :3 with inner product given by the usual dot product, and let T e L(V) be given by 71:1, 32 z3) = (Z3, 2Z2, Z1) a) Find a formula for the adjoint T' b) Is Tself adjoint? ls T normal? Explain. c) Find an orthonormal basis of V in which MO") is diagonal, if this is possible, or else explain why not if this is not possible