Consider a quantum system with an observable a that has three possible measurement results: a_1, a_2, and a_3. write down the three kets |a_1), |a_2), and |a_3) corresponding to these possible results using matrix notation. the system is prepared in the state |psi) = 1|a_1) - 2|a_2) + 5|a_3) write this state in matrix notation and calculate the probabilities of all possible measurement. results of the observable a in a different experiment, the system is prepared in the state |psi) = 2|a_1) + 3i|a_2). write this state in matrix notation and calculate the probabilities of all possible measurement results of the observable a