# 09-240/On The Final Exam

Our final exam is coming up. It will take place at BN2S - room 2S of the Clara Benson Building, 320 Huron Street (south west of Harbord cross Huron, home of the Faculty of Physical Education and Health) on Wednesday December 16 from 9AM until 12noon. It will consist of 5-6 questions (each may have several parts) on everything that we have covered in class this semester:

• Fields and vector spaces.
• Spans, independence, replacement and bases.
• Linear transformation, rank, nullity, matrices, change of basis.
• Row and column reduction and elementary matrices, systems of linear equations.
• Determinants.
• Several other "smaller" topics.

As for the style -

• You can expect to be asked to reproduce some proofs that were given in class.
• You can expect some fresh things to prove, though generally not as hard as the previous type of proofs.
• You can expect questions (or parts of questions) that will be identical or nearly identical to questions that were assigned for homework.
• You can expect some calculations (but nothing that will require a calculator).

It is likely that the exam will be close in spirit to the exam of three years ago, yet without the parallel of 2006 question 5. See 06-240/The_Final_Exam.

Basic calculators (not capable of displaying text or sounding speech) will be allowed but will not be necessary. You may wish to bring one nevertheless, as under pressure ${\displaystyle 5+7}$ often comes out to be ${\displaystyle 13}$.

Remember. Neatness counts! Organization counts! Language counts! Proofs are best given as short and readable essays; without the English between the formulas one never knows how to interpret those formulas. When you write, say, "${\displaystyle v\in V}$", does it mean "choose ${\displaystyle v\in V}$", or "we've just proven that ${\displaystyle v\in V}$", or "assume by contradiction that ${\displaystyle v\in V}$", or "for every ${\displaystyle v\in V}$" or "there exists ${\displaystyle v\in V}$"? If you don't say, your reader has no way of knowing. Also remember that long and roundabout solutions of simple problems, full of detours and irrelevant facts, are often an indication that their author didn't quite get the point, even if they are entirely correct. Avoid those!

Office hours. Our TA Alan Lai and I (Dror) will hold four sessions of extended office hours as follows:

• Dror: Friday December 11th, 9-12, at or near Bahen 6178.
• Alan: Monday December 14, 6-8, at the TA Consultation room, Bahen 6283.
• Dror: Tuesday December 15th, 1-4, at or near Bahen 6178.
• Alan: Tuesday December 15th, 5-8, at the TA Consultation room, Bahen 6283.

Here is a link to the exam forum: Final Exam Preparation Forum