5. (Optional) We are given p matrices A; E Roxn , and we would like to find a single matrix X E Rox" that we can use as an approximate right-inverse for each matrix A; , i.e., we would like to have A;X ~ I,i = 1,...,p. We can do this by solving the following optimization problem with X as variable: minimize max | |/ - AXIl. (1) i=1,....P Here | | H | | is the 'infinity-norm' or 'max-row-sum norm' of a matrix H, defined as n IIHloo = max i=1,...,m j=1 if H E Rmxn. Express problem 1 as an LP. You don't have to reduce the LP to a canonical form, as long as you are clear about what the variables are, what the meaning is of any auxiliary variables that you introduce, and why the LP is equivalent to the problem 1