Exam 3 will cover Chapters 6 and 7 (Determinants, Eigenvalues) of Bretscher (any edition). As always, one can work problems from the text for additional practice.
For Exam 3, one should be able to
Compute a determinant, using the formula, expansion by minors, row reduction, and/or computing recursively from smaller cases, as appropriate.
Apply Cramer’s rule
Invert a 3 x 3 matrix
Find the nth power or the exponential of a 2 x 2 matrix with distinct eigenvalues
I have posted a practice exam 3 which gives examples of problems of these forms:
Some of these problems may be beyond the scope of our Exam 3.
I have generated a new atlas of eigenvalue problems that can be worked by hand.
The original atlas is still available. It does not include any 3 by 3 repeated root problems.
This page hosts the above files, and many other PDF files from previous semesters.