Last Updated:  December 1, 2017

Math 2085
Linear Algebra
Spring 2017

## Daily Schedule

Class Date Topic Section Problems from book
1 Aug 21 Gauss's Method
One.I.1
1.17,  1.19, 1.22, 1.24, 1.27
2 Aug 23 Describing the Solution Set
One.I.2
2.15, 2.16, 2.17, 2.18, 2.21, 2.25, 2.29
3 Aug 25 General = Particular + Homogeneous
One.I.3
3.15, 3.17, 3.18, 3.20, 3.24
4 Aug 28 Gauss-Jordan Reduction
One.III.1
1.8, 1.10, 1.12, 1.14, 1.15
5 Aug 30 The Linear Combination Lemma
One.III.2
2.11, 2.14, 2.20, 2.22
6 Sept 1 Definition of Vector Space
Two.I.1 1.17, 1.18, 1.19, 1.21, 1.22, 1.28
7 Sept 6 Examples of Vector Spaces
Two.I.1, 2
2.20, 2.21, 2.23, 2.25, 2.26, 2.27, 2.29
8 Sept 8 Subspaces and Spanning Sets
Two.I.2

9 Sept 11 Linear Independence
Two.II.1
1.20, 1.21, 1.23, 1.24, 1.27
10 Sept 13 Basis
Two.III.1
1.18, 1.19, 1.20, 1.24, 1.25, 1.28, 1.19, 1.37
11 Sept 15 Review

12 Sept 18 Exam 1

13 Sept 20 Dimension of Vector Space
Two.III.2
2.16, 2.18, 2.21, 2.22, 2.26
14 Sept 22 Dimension
Two.III.2, 3

15 Sept 25 Vector Spaces and Linear Systems
Two.III.3
3.17--3.21, 3.23, 3.24, 3.29, 3.32
16 Sept 27 Definition and Examples of Isomorphism
Three.I.1
1.12, 1.13, 1.17, 1.21,1.23, 1.24
17 Sept 29
Three.I.1

18 Oct 2 Dimension characterizes Isomorphism
Three.I.2
2.9, 2.10, 2.11, 2.12, 2.14, 2.15
19 Oct 4
Three.I.2

20 Oct 6 Homomorphisms
Three.II.1
1.18, 1.19, 1,20, 1.25, 1.26, 1.31
21 Oct 9 Range and Null Space
Three.II.2
2.21, 2.23, 2.24, 2.25, 2.30, 2.33, 2.35
22 Oct 11
Three.II.2

23 Oct 13 Review

24 Oct 16 Exam 2

25 Oct 18 Linear Maps via Matrices
Three.III.1
1.12, 1.18, 1.21, 1.26, 1.29, 1.33
26 Oct 23 Matrix representation of linear map
Three.III.2
2.14, 2.15, 2.16, 2.22
27 Oct 25 Matrix sum and scalar product
Three.IV.1, 2
1.8, 1.18, 2.14, 2.15, 2.17, 2.19, 2.21, 2.33
28 Oct 27 Matrix multiplication
Three.IV.2, 3
3.24, 3.25, 3.28, 3.29, 3.32, 3.34, 3.41
29 Oct 30 Inverse of matrix
Three.IV.4
4.13, 4.14, 4.15, 4.17, 4.18, 4.20, 4.28, 4.34
30 Nov 1 Basis representation
Three.V.1
1.7, 1.9, 1.10
31 Nov 3

32 Nov 6 Determinants
Four.I.1
1.1, 1.3, 1.4, 1.7, 1.9, 1.15
33 Nov 8 Properties of determinants
Four.I.2
2.8, 2.9, 2.12, 2.13, 2.15, 2.18
34 Nov 10 Laplace expansion
Four.III.1
1.11, 1.12, 1.14, 1.16
35 Nov 13 Review

36 Nov 15 Exam 3

37 Nov 17 Matrix similarity
Five.II.1
1.8, 1.9, 1.10, 1.11
38 Nov 20 Diagonalizability
Five.II.1, 2
2.6, 2.7, 2.14, 2.15, 2.17
39 Nov 22
Five.II.2

40 Nov 27 Eigenvalues and Eigenvectors
Five.II.3
3.21, 3.22, 3.23, 3.25, 3.26, 3.27, 3.28, 3.32
41 Nov 29

42 Dec 1 Review

### Homework Assignments

 Homework Assignment (to turn in) Due  Date Solutions Homework #1 Aug 28 Solutions Homework #2 Sept 6 Solutions Homework #3 Sept 15 Solutions Homework #4 Sept 27 Solutions Homework #5 Oct 4 Solutions Homework #6 Oct 13 Solutions Homework #7 Oct 30 Solutions Homework #8 Nov 6 Solutions Homework #9 Nov 13 Solutions Homework #10 Nov 29 Solutions

### Exam Reviews

Exam 1 Review  With Solutions
Exam 2 Review  With Solutions
Exam 3 Review  With Solutions

### Exams

Exams Date Solutions
Exam 1 September 18 Solutions
Exam 2 October 16 Solutions
Exam 3 November 15 Solutions
Final Exam December 8  (10:00 - 12:00 ) Solutions