Week 3: February 23-27

Chapter 2.3 Inverse of a linear transformation

Key points: a) Definition of an invertible function

b) Non-invertibility if the matrix is not square.

c) Explain how Fact 2.3.5 arises

d) Don’t worry to much about determinants yet—can skip this if out

of time.

Homework: 12, 20, 30, 38, 40, 41*, 44*

Chapter 2.4 Matrix products

Key points: a) Terminology: The composite of two functions. Note that the

domain of the second must be the codomain of the first.

b) Definition of matrix multiplication. Terminology: AB

c) Non-commutativity. Associativity, multiplying by identity,

mutliplying by the inverse, inverse of a product.

d) Summation formula, convention with repeated indices.

Homework: 14, 28, 38, 56, 76, 33*, 80*

Chapter 3.1 Image and kernel

Key points: a) Vocabulary: Image, kernel, span.

b) Span of a set of vectors.

c) Properties of the kernel, 3.1.6.

Homework: 2, 20, 32, 34, 44, 54, 37*, 50*