------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.