Consider the s- operator (the spin operator in the z-direction), and the sy operator (the spin operator in the y-direction). a. in the z-basis: i. what is s, in matrix format? what is the z+ state in matrix format? show that z+ state is an eigenvector of sz. what is the eigenvalue? iii. what is sy in matrix format? iv. what is the y+ state in matrix format? show that y+ state is an eigenvector of sy. what is the eigenvalue? v. show that z+ state is not an eigenvector of sy. vi. show that y+ state is not an eigenvector of sz. b. in the y-basis: i. what is sy in matrix format? ii. what is the y+ state in matrix format? show that y+ state is an eigenvector of sy. what is the eigenvalue? is the y+ state in the y-basis, the same state as the y+ state in the z-basis? explain. iv. is the sy operator in the y-basis, the same state as the sy operator in the z-basis? explain.