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 ||Axb||². In the second problem we remove column i of A or, equivalently, set x = 0: (1) minimize subject to ex Ax-b||2 0. (2) Here e, 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=- Îi ((ATA)-¹)ii (ATA)-¹ei. (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 î 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).