Problem 2. (mar. 20 : 104-10 points) (a) Find all orderings/reorderings 63,, 61-2, 82'3 of the standard basis vectors 61 = (1, 0, 0), 82 = (0, 1,0) and 63 = (0,0,1) in R3 for which we will have: the ordered basis {6,,, 81'2, 6,3} induces the canonical orientation on R3, that is, the same orientation as the one induced by the ordered basis {61, 62, 63}. Note that, obviously, one of these orderings is the trivial one, that is, the case where we don't change the order of any of the standard basis vectors, and just recover the ordered basis {81, 62, 63} (that would be what we call in Mathematics the \"d6ntity permutation\"). So you are essentially asked to nd all the other orderings with the required property, the nontrivial permutations, and also to justify that the ones you will list are the only orderings of 61, 62, 63 with the required property. (b) Which of the following ordered bases of R3 induce the canonical orientation? \\Vhich induce the opposite orientation? Show all your work. 31 Z {'31 + 82181 _ '32: 63}: B2 = {61 62181 + 62, 83}, 53 = {81, 61 + 62, 81 + 82 + 63}: B4 = {62 61, 82 83: 61 + 63}