The operator in matrix form is given by
An eigenspinor of with eigenvalue must satisfy
We can convert all of the answers to vector notation by using the identifications
We can then check whether the condition in equation (1) is satisfied. We find that it is satisfied only for answer (C). Therefore, answer (C) is correct. Physically, this means that the eigenspinor in answer (C) represents a particle with definite -component of its spin vector equal to .