Problem 4 [15 points} Linear programming {LP} problems and leastsquares problem are both special cases of the general convex optimization problem. An LP problem is an optimization problem with constrains; a leastsquares problem is an optimization problem with no constrains. For a leastsquares problem, the objective function is of the form: minimize error f[;r} = \"Arr b\"; = 2(333 5,}2. i=1 Here, the vector I E R" is the optimization variable, and b E IR\" also. Differentiating with respect to It. and imposing the condition for a critical point as \"VI = U, the solution of the above leastsquares problem can be reduced to solving a set of linear equations, {Au}: = ATE: Hence we have the solution I = {ATA}_1{AT-tr}, {for nonsingular problems}. 1. Find the least squares solution for the system {AI = :5}: III11:2 =2 .'I.'1+."Eg =4 Ell-FIE =3. 2. W'hat is the error