Assume that T L(V ) and that its matrix relative to to the basis v1 = (1, 0, 1), v2 = (1, 0, 1), v3 = (0, 1, 0) in both the domain and codomain of T is denoted by A. Also assume that

T(1, 0, 1) = 2(1, 0, 1), T(0, 1, 0) = 2(0, 1, 0), T(0, 1, 1) = (1)(0, 1, 1).

Observe that the eigenvectors in this case are also a basis different from v1, v2, v3. Find the matrix P such that [P ^(1)]AP = D is diagonal. Use this information to find A.