ANSWER ONLY IF YOU KNOW, DO NOT COPY FROM CHEGG, I HAVE SEEN THEM ALL. ANSWERS ARE WRONG...,,

Bonus Problem: Let A be a real m x n matrix with linearly independent columns, and let b be a real m-vector. We consider two least-squares problems. The first problem is the standard minimize ||Ax b|| (1) In the second problem we remove column i of A or, equivalently, set xi = 0: minimize || Ax b||2 (2) subject to ex = 0. Here ei denotes the ith unit vector of length n (an n-vector with all its elements zero, except the ith element, which is one). (a) Let be the solution of (1). Show that the solution of (2) is x = c i -(A? A)-fei. ((AT A)?)ii (3) The denominator in the second term is the ith diagonal element of the inverse (ATA)-1. (b) Describe an efficient algorithm, based on the QR factorization of A, to calculate and the vector x in (3). Carefully state the different steps in your algorithm, and give the complexity of each step (number of flops for large m, n)