Question 3 Illustrate the following: 3) Suppose the utility that one receives from consuming Goods A and B can be either positive or negative, represented by a vector u(nA,uH). When the consumption is enjoyable, the utility is positive and when the consumption becomes a burden, the utility becomes negative. Consider 2 utility combinations Hi and uz , where H1 2 (4,1) and u: = {2,3). Illustrate the difference between these two utility levels in a 2-dimensional setting. [5 Marks] b) Expand the setting in Part 1] to a 3-dimensional case, i.e. there now exist 3 2 I] I] commodities A, B and C. Given 3 utility levels 111 = [01, u: = [31 and 113 = []. 2 U D depictthe vector 2111 + n2 + 2113. [5 Marks] Question 4 Prove the following: a} 233:1 abjyj = o Elia by; [4 Marks] 5} ELK-T; + 15:) = 33:11; + 233:1}? [4 Marks] c) For a given matrix A, its inverse matrix must be unique if it exists at all. [5 Marks] :1} (:t')'1 = (141)\" [5 Marks]