My solution attached.

NOTE that there is a typo in the statement of this exercise: The second-last line should actually read:

Quote:

"...then the dimension is an integer 2j+1, where..."

Currently it states that the dimension is 2

j rather than 2

j+1.

This is incorrect, because the main text says that

m runs from -

j to

j, so it has 2

j+1 possible values; and it is stated that

has 2

j+1 independent components. My solution also arrives at 2

j+1 as the dimension of the representation space.