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.