Problem 4 (15 points) Linear programming (LP) problems and least-squares problem are both special cases of the general convex optimization problem. An LP problem is an optimization problem with constrains; a least-squares problem is an optimization problem with no constrains. For a least-squares problem, the objective function is of the form: minimize error f(x) = ||A.c 6112 = (oz-b;)?. i=1 Here, the vector IER" is the optimization variable, and be Rn also. Differentiating with respect to Ik and imposing the condition for a critical point as Vf = 0, the solution of the above least-squares problem can be reduced to solving a set of linear equations, (ATA).= Ab Hence we have the solution r = (ATA)- (Ab), (for nonsingular problems). 1. Find the least squares solution for the system (Ac = b): 11 - 12 I1+I2 (2.61 + 12 = 2 = 4 = 8. 2. What is the error