# Math 110 — Linear Algebra

Date Topic Book Homework Practice Problems
Jan. 10 Introduction to determinants
12 Axiomatic characterization of the determinant
13 Bilinearity and determinants in ℝ2
17 Trilinearity and determinants in ℝ3 §4.2
19 The determinant in any dimension §4.2
20 Permutations and the determinant formula §4.2 H13
24 Calculating the determinant §4.2 A13 1 – 15
26 More determinant calculations §4.2 16 – 20, 22, 23, 26 – 29
27 Cramer's Rule §4.2 H14 35 – 38, 57 – 60
31 The classical adjoint §4.2 A14 61 — 64
Feb. 2 Bases and coordinates §6.3 1, 2, 3, 4 (part a only)
3 Change of basis §6.3 H15 1, 2, 3, 4 (parts b, c, d, e)
Feb. 7 Change of basis II   A15
9 In-class exam #3
10 Iterating linear transformations §3.7 H16 5 – 8, 10
14 Eigenvalues and Eigenvectors §4.3 A16 §4.1: 13–17
16 Finding Eigenvalues and Eigenvectors §4.3 1–6 (parts a and b)
17 Diagonalization §4.4 H17 5–7
21
24
28 Eigenspaces §4.3 A17 1–6 (parts c and d)
Mar. 2 More Diagonalization §4.4 8–15, 16–18
3 End of the proof on Diagonalization §4.4 H18
7 Complex Numbers App. C A18
9 Complex Eigenvalues and Eigenvectors
10 Dominant Eigenvalues §4.5 H19 9–12
14 The Gerschgorin disk theorem §4.5 A19 47–50
16 In-class exam #4
17 Some Eigenapplications §4.6 H20 7–9
21 Introduction to abstract vector spaces §6.1 A20 5–10
23 Subspaces, bases, coordinates §6.1-2 §6.1: 29, 33, 35, 36
24 Linear transformations §6.4 H21 5, 7, 8, 16
28 Dimension, Rank-nullity theorem §6.5 A21 3, 4, 10, 12
30 Inner product spaces §7.1 1, 2, 5, 9, 10, 11
31 Orthonormal bases §5.1 H22 1–6, 11–15
Apr. 4 Gram-Schmidt orthogonalization §5.3 A22 1–6, 11, 12
6 Least-squares solutions §7.3 19, 20, 23, 24
7 Least-squares solutions II §7.3 H23
11   A23
13   H24
14   A24