## Plan

- Finish Chapter 3
- Start motivating determinants
- Quiz

## Chapter 3

- Do example from midterm. Both range and nullspace.

## Determinants

- Determinant is a function whose magnitude is tells you about change in volume and whose sign tells you about change in orientation.
- Determiant as a function on the columns.
- Determinant is the unique n-linear alternating function whose value on the identity is 1.
- identity is reasonable.
- n-linear is reasonable.
- alternating is reasonable.
- if alternating then the switching.