The total mark is 72. The marks breakdown is as follows: PS#2 7 Q1(b) 7 Q1(d) 8 Q1(3) 4 Q6 4 Q8(a) 4 Q8(b) Total: 34 PS#3 6 Q1(1b) 6 Q1(1d) 7 Q1(3) 5 Q3 6 Q5 4 Q7(a) 4 Q7(b) Total: 38 34+38 is 72 Comments from the markers: A LOT had problems with PS#2 Q3 and the corresponding part in PS#3. Confused on how to deal with the C^2-space. Some treated it as 2-d but neglected to allow complex numbers; some treated it as a 4-d space but lost track of what they were trying to find and were not sure how to integrate their results back to complex numbers in 2-d... etc. A number of the proofs, although the basic idea was there, they failed to present them well in a logical fashion (A leads to B which leads to C because of... etc). Instead... a lot were like, "We know that A, B, C... and since D, E, F... then G is true" when the actual result was not-so-obvious. Very surprisingly, many did not realize that if the null space is not empty then the transformation cannot be 1-1! They used very lengthy methods to show so. PS#3 question 3, many neglected to show that their transformation was linear (in a number of cases they were not) PS#3 question 5, majority of the proofs were generally quite poor but attempted nonetheless since it is quite easy to visualize why the result is so. Many showed that a vector v from V is also in W and claimed V=W, when all they have shown is that V is a subset of W. PS#3 question 7, a lot did not understand what the question was asking, they instead proved that T: R^3 -> R as defined by T(x,y,z) = (a,b,c)(x,y,z) is a linear transformation.