Exam III will be in the usual classroom on Wednesday, April 28, 2010. It will cover sections 4.8, 6.1-6.3, and 3.1-3.3. The current draft has 52 points possible. 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. Many 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.

Note that the exam will not cover inner products (chapter 5) or the adjoint matrix (section 3.4), although these will be covered on the final exam. Exam III is roughly 30 points on coordinates, linear transformations, kernel and range, and representations of linear transformations, and about 20 points on determinants. You will need to be familiar with the definition of determinant, as well as with the general properties of the determinant function. The following topics are very likely to appear, although the exam is not limited to these topics:

1. Coordinate vectors and transition matrices.
2. Linear transformations. Definition, verifying that a function is or is not a linear transformation, examples.
3. Kernel and range of a linear transformation.
4. Matrix representations of linear transformations. Be able to compute them, and understand what they say in terms of coordinates ( i. e. A v_S=(L(v))_T ). Understand how to use matrix representations to find the kernel and range of a linear transformation.
5. The determinant. Know and understand the defining formula. Properties of the determinant, such as det(AB)=det(A) det(B) and its relation with nonsingularity.
6. The effect of elementary row operations on the determinant. Applications to computing determinants.
7. Cofactors and expansion of the determinant using cofactors. Applications to computing determinants.

Topics and techniques in the book that we did not examine in class or in homework will not be covered.

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.