Consider the loo-regression problem. Given an n x d matrix A, n > d, and an n x 1 vector b. We would like to find an x e Rd which minimizes the the quantity max=1 |(A, x) bil, which is sometimes denoted ||Az b||20. Note that for two vectors u and v of length d, the notation (u, v) = !=jui V; denotes their dot product. = d i=1 (a) Write the linear program to model the problem minzerd ||A, b||20. Your linear program should be in standard form. You do not need to prove correctness. (b) Consider the 1-norm, denoted ||X||1, and defined by ||X||1 =147) and the objective function min ||Aq b||00 + 1||X||1, = d i= XER where 1 > 0 is a given constant. Write the linear program to model this problem. Your linear program should be in standard form. You do not need to prove correctness. (c) Suppose in the previous part we instead have i d, and an n x 1 vector b. We would like to find an x e Rd which minimizes the the quantity max=1 |(A, x) bil, which is sometimes denoted ||Az b||20. Note that for two vectors u and v of length d, the notation (u, v) = !=jui V; denotes their dot product. = d i=1 (a) Write the linear program to model the problem minzerd ||A, b||20. Your linear program should be in standard form. You do not need to prove correctness. (b) Consider the 1-norm, denoted ||X||1, and defined by ||X||1 =147) and the objective function min ||Aq b||00 + 1||X||1, = d i= XER where 1 > 0 is a given constant. Write the linear program to model this problem. Your linear program should be in standard form. You do not need to prove correctness. (c) Suppose in the previous part we instead have i