using the below to setup the optimization problem for finding the third principal component direction for a data matrix X. Prove that the variance in this direction is the third largest eigenvalue of the covariance matrix. kindly provide all steps for my understanding. thank you N maximize Var(2 a,X,) = aJr S a. such that a! a = I. l=[ u Or equwalenlly. by usmg Lagrange-'5 optimization method [find stationary points} Em. A] = (115:: it\"! a I) such that! (1'0 2 l