Information about the Final Exam for Math 3333-002

Mathematics 3333-002 - Linear Algebra I - Spring 2010

Information about the Final Exam

The Final Exam will be in the usual classroom at 8:00 a. m. on Tuesday, May 11, 2010. The current draft has 80 points possible. You may work until 10:15 a. m., and (assuming that you have a reasonable knowledge of the subject) you should have no difficulty completing the exam in that amount of time.

Please do not stay up late trying to study at the last minute. This usually costs more than it gains, sometimes much more. Just study the topics emphasized below during the few days before the exam, and show up well-rested and relaxed.

The exam format will be similar to the in-class exams, except that there will be one section of true-false questions. For these, write T or F in the spaces on the exam itself. For the other problems, put your solutions on the additional paper that will be provided as usual.

Calculators or any electronic gear are not needed and are not to be used during the exam.

The following topics are definitely covered on the exam, although it is not limited to them:

  1. Solution of linear systems by Gauss-Jordan elimination and back substitution.
  2. Elementary matrices and their relation to row operations.
  3. Spanning, linear independence, and bases. These are fundamental ideas in linear algebra.
  4. Linear transformations, matrix transformations, kernels, ranges.
  5. Inner products, orthogonal and orthonormal sets of vectors.
  6. Coordinate representations, transition matrices, representation of linear transformations as matrix transformations. This takes some work, but it is important.
  7. Eigenvalues, eigenvectors, characteristic polynomials, similarity and diagonalization. These will receive extra weight, probably around 20 points, since they were not covered on the in-class exams. And they are important ideas.

The determinant will appear but receives fairly minimal coverage. Cofactors are not a major topic, although you should be using them when computing determinants.

Topics and techniques in the book that we did not examine in class or in homework will not be covered. The following topics do not appear: definition (axioms) of a vector space, verifications of properties (such as associativity or distributivity) of matrix operations, equivalence of matrices (B = PAQ for nonsingular P and Q), adjoint matrices, inner products defined using integrals.

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).

1. Solution of linear systems by Gauss-Jordan elimination and back substitution.
2. Elementary matrices and their relation to row operations.
3. Spanning, linear independence, and bases. These are fundamental ideas in linear algebra.
4. Linear transformations, matrix transformations, kernels, ranges.
5. Inner products, orthogonal and orthonormal sets of vectors.
6. Coordinate representations, transition matrices, representation of linear transformations as matrix transformations. This takes some work, but it is important.
7. Eigenvalues, eigenvectors, characteristic polynomials, similarity and diagonalization. These will receive extra weight, probably around 20 points, since they were not covered on the in-class exams. And they are important ideas.