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Let T ∈ L(C3) be the operator given by T(z1,z2,z3)=(z1 +z2 −2z3,z1 +z2 −2z3,z1 +z2 −2z3)....

  1. Let T ∈ L(C3) be the operator given by
    T(z1,z2,z3)=(z1 +z2 −2z3,z1 +z2 −2z3,z1 +z2 −2z3).

    Find a basis of C3 such that M(T ) is block diagonal with upper-triangular blocks (as guaranteed by 8.29) and write the matrix M(T ) in this basis.

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