Lecture 
Date 
Section Covered 
1 
09/07 
1.1, 1.2 Matrices and Vectors 
2 
09/11 
1.3 Systems of Linear Equations 
3 
09/14 
1.4 Gaussian Elimination 
4 
09/18 
1.6 Span of a Set of Vectors 
5 
09/21 
1.7 Linear Dependence and Linear Independence 
6 
09/25 
1.7, 2.1 Homogeneous Systems, Matrix Multiplication 
7 
09/28 
2.1 Matrix Algebra;
Quiz 1 
8 
10/02 
2.3,
Appendix E Invertibility and Elementary Matrices, Uniqueness of RREF 
9 
10/05 
2.4
Inverse of a Matrix 
10 
10/09 
2.6 LU Decomposition of a Matrix; Review for the exam 
11 
10/12 
Midterm Exam 1 
12 
10/16 
3.1 Determinants; Cofactor Expansions 
13 
10/19 
3.2 Properties of Determinants 
14 
10/23 
4.1 Subspaces 
15 
10/26 
4.2 Basis and Dimension 
16 
10/30 
4.3 Column Space and Null Space of a Matrix 
17 
11/02 
5.1 Eigenvalues and Eigenvectors;
Quiz 2 
18 
11/06 
5.2 Characteristic Polynomial 
19 
11/09 
5.3 Diagonalization of a Matrix 
20 
11/13 
5.5 Applications of Eigenvalues;
Review for the exam 
21 
11/16 
Midterm Exam 2 
22 
11/20 
6.1 Geometry of Vectors; Projection onto a Line 
23 
11/21 
6.2 Orthogonal Sets of Vectors; Gram
 Schmidt Process; QR factorization 
24 
11/27 
6.3 Orthogonal Projection; Othogonal Complements 
25 
11/30 
6.4
, 6.5 Least Squares, Normal Equations,
Orthogonal Matrices 
26 
12/04 
6.6 Diagonalization of Symmetric Matrices

27 
12/07 
6.6 Spectral Decomposition for Symmetric Matrices, Diagonalization of Quadratic Forms 
28 
12/11 
Review for the Final Exam 