2. (20 points. This problem is set-up for the next problem, which will involve implementation of search heuristics You may remember systems of equations from your muth classes. They are different equations of variables. For example, is a system of M - 2 equations with N-2 unknown variables (ands). The goal is to find values of the variables, and that make the equations in the system true. Soly ing systems of equations when the variables x are real valued is relatively straightforward solving them when x are restricted to be binary values (that is, oor ) is hard. That is, while it may not seem intuitive, allowing each for 1.... to be only either or I makes the problem difficult to solve efficiently While it's convenient, it is not required. For example, is a system of 2 equations with N = 3 unknown variables. In general. a system of equations can be written as +++ 3+3++y MIN The aim are the coefficients, and are the required output values. If we use matrix-vector notation, where the matrix (2-4 array) A stores the coefficients, the one dimensional vector (array) x stores the variables and the one dimensional vector array) y stores the output values aux M 192 ON WM then with matrix-vector multiplication we can write compactly as Axy (a) For the following system of equations with binary variables, identify A and y. Addi tionally, provide the solution for x Gas a hint, the variables are x =) +44 (2) (b) Construct an unsatisfiable system of equations with binary variables. That is write out A and y such that there's no possible binary that will make Ax - y true. Briefly explain why this is an unsatisfiable system (c) Construct a system of equations with binary variables that has multiple possible solo tions. That is, write out A and y such that there is more than one binary x that will make Ax = y true. Provide at least two of these values of x (d) If you were to construct an agent for this problem, identify/describe c) the environment (m) the state () actions your agent may take, along with any possible constraints on those actions Gv) possible costs associated with your actions (v) the goal goal test predicate As a hint there is not a correct answer for the possible costs. Additionally, the goal/Goal test predicate must not assume any correct" values of it must work for ay binary baride