# Math 417

Midterm 2 Study Guide

Winter 2008

### Content

The material will be drawn from Sections 3.3 and 3.4, and from Sections 5.1, 5.2 and 5.3. You will want
to review homework problems as well as the material below. You will find solutions to the odd problems (including True/False problems) on Otto Bretscher's website:

`http://www.colby.edu/personal/o/obretsch/ssm/`
### Computational Problems

- Computing coordinates for a vector in a given basis. Exercises 1 - 18 of Section 3.4
- Computing a matrix for a transformation relative to a given basis.
Exercises 19-30 of Section 3.4
- Computing the orthogonal projection, Exercises 26-28 of Section 5.1. You will need to know
how to use Fact 5.3.10.
- Gram-Schmidt Orthonormalization. Exercises 1-14, 29-35 of Section 5.2.

### Conceptual Problems

- Chapter 3 True/False Problems: 12, 15, 27, 29, 30, 37, 40, 42, 43, 44, 45, 49, 50, 51, 52.
- Orthogonal matrices: Exercises 5-11 of Section 5.3.
- Chapter 5 True/False Problems: 1, 4, 6, 9, 13, 17, 20, 28, 31, 38, 44, 45.