Please answer with explanation

Consider a Hilbert space {|1), I2), |3)} An observable is represented in this space by an operator that reads, as a matrix, A 0 l 0 A = 1 0 0 0 0 1 The ordering of row and column indices is I1), I2), I3). a) Write the operator in projector notation using Dirac bras and kets b) What are the possible measurement results? Find the normalized and orthogonal quantum states that will yield these results upon measurement with 100% certainty. Write the states in Dirac notation 3 M=Z%m, i=1 with i, j = 1, 2, 3 and coefcients cg,- that you are supposed to nd and to write out. What are the degeneracies of the possible measurement results? c) Assume an incident state hp) = i (ll) + |3)). What are the probabilities for the measurement results? What is the average measurement result? What is the variance, (mar All/1) = (1M (/1 (MA |))2|) of the measurement? d) What are the corre3ponding states after measurement? Give the states in Dirac notation in both the original basis and in the basis generated by A