Given the first and second principle component loading vectors !-[011,921]T , 12 and 22- (a) If two observations in the original data set are (xi1 1,x12 1) and (x21 -1 ,x22 -1), compute the values of the corresponding transformed observations, namely (z11,212) and (z21,22), in the transformed data set (whose feature space is characterized by the first two principle components). (b) If two observations in the transformed data set (whose feature space is char- acterized by the first two principle components) are (231 1,232 1) and (241- -1 , z42 =-1), compute the values of the corresponding original observations, namely (X31,X32) and (x41M42), in the original data set