Information about Exam I for Math 3333-001

Mathematics 3333-001 - Linear Algebra I - Spring 2009

Information about Exam I

Exam I will be in the usual classroom on Thursday, February 19, 2009. It will cover sections 1.1-1.6 and 2.1-2.2. There are 50 points possible.

Some of the exam problems will be very similar to homework problems, while others will draw upon the material presented in the lectures. 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.

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.

On the exam day, please sit with an even number of seats to the right of you in your row (that is, in alternating columns), so as not to be distracted by nearby students.

The following topics are very likely to appear, although the exam is not limited to these topics:

  1. Row echelon form and reduced row echelon form, using them to find the general solution of a system of linear equations (that is, Gaussian elimination and Gauss-Jordan elimination)
  2. Equivalence between a system of linear equations, a matrix equation of the form AX=B, and a vector equation of the form x_1C_1 + x_2C_2 + ... + x_nC_n=B (where C_1, ..., C_n are the columns of A).
  3. Properties of matrix operations and transpose.
  4. Singular and nonsingular matrices, inverses.
  5. Matrix transformations, linearity (that is, the property that F(aX + bY) = aF(X) + bF(Y)), geometric interpretation as reflections, rotations, projections, etc.

The following topics do not appear, at least not explicitly: solving systems of linear equations the old-fashioned way (that is, as in section 1.1), partitioned matrices (other than augmented matrices, which are one example of them), mutual funds examples, pivots.

Exams from previous classes I have taught can be found on their course pages (links to them appear on the course pages page). Some were 50-minute classes, but most were 75-minute classes. Unfortunately I have not taught Math 3333 since we went online, so there are no old exams available, but looking at some of the calculus class exams may give you a feel for my exam style and format.

1. Row echelon form and reduced row echelon form, using them to find the general solution of a system of linear equations (that is, Gaussian elimination and Gauss-Jordan elimination)
2. Equivalence between a system of linear equations, a matrix equation of the form AX=B, and a vector equation of the form x_1C_1 + x_2C_2 + ... + x_nC_n=B (where C_1, ..., C_n are the columns of A).
3. Properties of matrix operations and transpose.
4. Singular and nonsingular matrices, inverses.
5. Matrix transformations, linearity (that is, the property that F(aX + bY) = aF(X) + bF(Y)), geometric interpretation as reflections, rotations, projections, etc.