# Math 417

Final Study Guide

Winter 2008

### Content

The exam will emphasize Chapters 6 (Sections 1,2) and 7; but it will include material from
Chapter 5 (Sections 1,2).
Solutions to the odd problems (including True/False problems) can be found on Otto Bretscher's website:

`http://www.colby.edu/personal/o/obretsch/ssm/`
### Chapter 5: Orthogonality

Review material from Section 1 and Section 2 (Gram-Schmidt process); you will need to be able produce
orthonormal bases using the Gram-Schmidt process. Review properties of the
transpose of a matrix, especially Fact 5.3.9. The exam will **not** cover orthogonal matrices from
Section 3.

### Chapter 6: Determinants

The exam covers Section 1 and 2 only.

- Section 1: 11-22.
- Section 2: 11-16, 39, 43, 46, 47, 48, 49.
- True/False: 8, 12, 14, 15, 23, 28, 33, 35, 38, 39, 40, 46.

### Chapter 7: Eigenvalues and Eigenvectors

The exam covers all sections.

- Section 2: 1-13.
- Section 3: 1-18, 19, 20.
- Section 4: 1-20, 21-30.
- Section 5: 20-26, 29, 45-50.
- Section 6: 1-10, 11-16, 17-24.
- True/False: 14, 18, 27, 32, 40, 44, 48, 51, 55, 56.