Construct, by applying the up and down steps, the matrices that represent to operators L?, L, Ly, L in the subspace generated by the base{|1, 1), |1,0), 1, -1)} of self-states of L? & .. Explicitly verify by multiplying the matrices the relation [,, L] = iL. 6. %3D (a) Find the base |1, m,) of self-states of i L, of said subspace. Write it as linear combination of 1, m). (b) Let a state be described by the vector T) = (11, 1) |1,1)). If measured L, What values can be obtained and with what probabilities? Repeat the calculation if measure Ly. (c) About the state l) is measured L, and is obtained h, and immediately after it is measured Ly. What values can be obtained and with what probabilities?