Week Topics Covered
1

1 - Linear Equations and Matrices
1.1 Systems of Linear Equations
2

1.2 Matrices
1.3 Matrix Multiplication
1.4 Algebraic Properties of Matrix Operations
3

2 - Solving Linear Systems
2.1 Echelon Form of a Matrix
2.2 Solving Linear Systems
4

2.3 Elementary Matrices; Finding A-1
2.4 Equivalent Matrices
5

3 - Determinants
3.1 Definition
3.2 Properties of Determinants
3.3 Cofactor Expansion
6

3.4 Inverse of a Matrix
7

3.5 Other Applications of Determinants
8

4 - Real Vector Spaces
4.1 Vectors in the Plane and in 3-Space
4.2 Vector Spaces
9

4.3 Subspaces
4.4 Span
4.5 Linear Independence
10

4.6 Basis and Dimension
4.9 Rank of a Matrix
11

4.7 Homogeneous Systems
4.8 Coordinates and Isomorphisms
12

5 - Inner Product Spaces
5.1 Length and Direction in R2 and R3
5.4 Gram-Schmidt Process
13

6 - Linear Transformations and Matrices
6.1 Definition and Examples
6.2 Kernel and Range of a Linear Transformation
14

6.3 Matrix of a Linear Transformation