Information about Exam II for Math 3333-002

Mathematics 3333-002 - Linear Algebra I - Spring 2010

Information about Exam II

Exam II will be in the usual classroom on Wednesday, March 24, 2010. It will cover sections 4.1-4.7 and 4.9. The current draft has 55 points possible, and many of the questions are easy. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others. Most of the questions will have rather short solutions, if you know how to do them, so if you find yourself doing something lengthy on a problem, it might be best to move on to other problems and come back later to it later if you have time.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with. Please write your solutions on the blank paper (you may have as many sheets as you need, and may put the problems in any order). Please hand in your exam paper along with your solutions.

Some of the exam problems will be similar to homework problems, while others will draw upon the material presented in the lectures. The following topics are very likely to appear, although the exam is not limited to these topics:

  1. Vector spaces and subspaces. Closure under addition and scalar multiplication. The eight defining properties (they need not be memorized, but understand what they say and be familiar with them). Verifying that a V does or does not satisfy a property.
  2. Span of a set of vectors, verifying that a subset spans. Linear dependence and independence, verifying that a set is linearly independent.
  3. Basis and dimension. You should be able to reproduce the major definitions--- not word-for-word, but at least equivalent to our given versions. How the dimension is related to spanning and linear independence (that is, the big pictures we discussed in class).
  4. Row, column, and null spaces of a matrix. Row rank and column rank, calculating the row rank. Rank plus nullity equals n, which is the number of variables of the homogeneous linear system AX=0. Rank plus nullity equals n.

Topics and techniques in the book that we did not examine in class or in homework will not be covered (what we did in class and homework is ample).

I have taught Math 3333 once since we went online at the turn of the millenium, and you can find the exams from that class at the course web page, linked at my course pages page). That class met twice a week, so the exams were geared to a 75-minute time period.

1. Vector spaces and subspaces. Closure under addition and scalar multiplication. The eight defining properties (they need not be memorized, but understand what they say and be familiar with them). Verifying that a V does or does not satisfy a property.
2. Span of a set of vectors, verifying that a subset spans. Linear dependence and independence, verifying that a set is linearly independent.
3. Basis and dimension. You should be able to reproduce the major definitions--- not word-for-word, but at least equivalent to our given versions. How the dimension is related to spanning and linear independence (that is, the big pictures we discussed in class).
4. Row, column, and null spaces of a matrix. Row rank and column rank, calculating the row rank. Rank plus nullity equals n, which is the number of variables of the homogeneous linear system AX=0. Rank plus nullity equals n.