1.1 Consider the following state vectors: 1)=3+)+ 4-) 1/2) = |+)+ 21-) 3)=3+) ei/3). a) Normalize each state vector. b) For each state vector, calculate the probability that the spin component is up or down along each of the three Cartesian axes. Use bra-ket notation for the entire calculation. c) Write each normalized state in matrix notation. d) Repeat part (b) using matrix notation for the entire calculation.