3. [22 points] We have derived the basis kets for the operators Sx, Sy and S, in terms of the basis kets +) of the S, operator. This problem involves using the transformation matrix to transform the basis kets to the Sy-basis. (a) [8 points] Construct the matrix that transforms from the Sz-basis to the Sy-basis. (b) [5 points] Prove that the transformation matrix is unitary. (c) [9 points] Use the transformation matrix to change the representation of the basis kets (+) |+) y, and (+) to the Sy basis. 3. [22 points] We have derived the basis kets for the operators Sx, Sy and S, in terms of the basis kets +) of the S, operator. This problem involves using the transformation matrix to transform the basis kets to the Sy-basis. (a) [8 points] Construct the matrix that transforms from the Sz-basis to the Sy-basis. (b) [5 points] Prove that the transformation matrix is unitary. (c) [9 points] Use the transformation matrix to change the representation of the basis kets (+) |+) y, and (+) to the Sy basis