In this exercise, I'm having trouble understanding how to compute the resulting state (point b). I don't understand how to do this kind of problem in general as well. Can you provide a detailed computation please?
One way to do a detailed computation is to write everything in the computational basis bra and kets, then expand all products, and apply the projector on the state. This has the disanvantage of being quite long. And at the end you recognize that what is happening is exactly what is written in the solution.
