(a) Find all eigenvectors and eigenvalues of the backward shift operator T in
End(R1) defined by
T(x1, x2, . . . ) = (x2, x3, . . . ).

(b) Find all eigenvectors and eigenvalues of T in End(Rn) defined by
T(x1, . . . , xn) = (x1 + x2 + + xn, 2x1 + 2x2 + + 2xn, . . . , nx1 + nx2 + + nxn).
Hint: Calculate the matrix corresponding to T and do examples for n = 2, 3.