## Exam 3 Preparation Linear Algebra Fall 2015

### Practice and Homework for Exam 3

Exam 3 will cover Chapter 6 and some of Chapter 7 (Determinants, Eigenvalues) of Bretscher (any edition). As always, one can work problems from the text for additional practice.

Specifically, be able to compute a determinant via the formula, expansion of minors, and/or row reduction. (A combination of methods is often fastest.) Be able to apply Cramerâ€™s Rule and compute inverses of matrices, by formula or quickly for 3x3 matrices. Be able to derive a recurrence relation for the determinant of a sequence of matrices, as seen in past exam problems. Be able to express a recurrence relation in terms of matrix multiplication. Be able to find the eigenvalues and eigenvectors of 2x2 and 3x3 matrices with distinct eigenvalues.

Homework is due at the latest by the start of our exam; it is in your interest to complete the homework sooner. Each problem will be scanned, graded, and returned as a PDF file. Collaboration on problems is encouraged, but each student must submit their own work.

Homework can be handed in online using your CourseWorks drop box, or in class, or using our math department homework box. Our homework box is on the fourth floor of the Mathematics building, on the left as one walks toward my office, 426 Math. Look for Bayer on our box; several students have lost homework by placing it in boxes for other sections of Linear Algebra.

I have posted a practice set with solutions, to serve as a model for completing this assignment.

Our exam will be similar to five of these nine problems.

Ideally, one should get far more practice than these problem sets offer. Your best bet is to look at course materials for previous semesters, many of which include solutions, and work as many similar problems as you can. Use your judgment in determining which past course materials are relevant.

A personalized copy of this assignment has been placed in your Courseworks Drop Box for this course. That copy includes a bar code identifying you and the problem, so that your work may be scanned, graded, and returned to you as a PDF file.

Please print out your personalized copy of this assigment onto standard letter-sized printer paper, and hand in only those sheets of paper. You may work on both sides of each sheet.

### Online Submission

If you would like to submit your homework online, please scan your work and upload the files to your CourseWorks Drop Box. If you do so, provide scans of a similar quality to my solutions above: 8.5 x 11, not twisted with respect to the page borders, and of sufficient resolution for your writing and the bar code to be clearly legible. You may use any file names and formats that you like, we will correspond by email if there is a problem.

You may use a phone or tablet app intended for scanning, or a campus copier that scans, or a dedicated scanner. My one requirement is that the edges of your paper align with the edges of your scan. Dedicated scanning apps will do this; ordinary cameras will not.

Do not return homework by email; I do not have an automated way to organize files received by email.

### Other Study Guides

You may find it useful to consult previous study guides for exam 3: