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Math 220: Linear Algebra

Spring 2023

Contents [Top]

Notes and Videos  [Top Contents]

Topic Blank workalong Completed workalong Videos Group Work
Introduction and Syllabus        

Chapter 1: Linear Equations in Linear Algebra

1.1: Systems of Linear Equations
1.2: Row Reduction and Echelon Form
1.3: Vector Equations
1.4: The Matrix Equation Ax=b
1.5: Solution Sets of Linear Systems
1.7: Linear Independence
1.8: Linear Transformations
1.9: Matrix of a Linear Transformation

1.1
1.2
1.3
1.4
1.5
1.7
1.8
1.9

1.1
1.2
1.3
1.4
1.5
1.7
1.8
1.9

1.1
1.2
1.3
1.4
1.5
1.7
1.8
1.9

1.1
1.2
1.3
1.4
1.5
1.6 and 1.7
1.8
1.9

Chapter 2: Matrix Algebra

2.1: Matrix Operations
2.2: Inverse of a Matrix
2.3: Characteristics of Invertible Matrices

2.1
2.2
2.3

2.1
2.2
2.3

2.1
2.2
2.3

2.1
2.2
2.3

Chapter 3: Determinants

3.1 & 3.2: Determinants



3.1 & 3.2

3.1 & 3.2

3.1/2 part 1 and 2

3.1/2

Chapter 4: Vector Spaces

4.1: Vector Spaces and Subspaces (subspace examples)
4.2: Null and Column Spaces, Linear Transformations
4.3: Linearly Independent Sets; Bases
4.4: Coordinates
4.5: Dimension and Rank
4.6: Change of Basis

4.1
4.2
4.3
4.4
4.5
4.6

4.1
4.2
4.3
4.4
4.5
4.6

4.1
4.2
4.3: video 1 and 2
4.4
4.5
4.6

4.1
4.2a and 4.2b
4.3
4.4a and 4.4b
4.5
4.6

Chapter 5: Eigenvalues and Eigenvectors

5.1: Eigenvectors & Eigenvalues
5.2: The Characteristic Equation
5.3: Diagonalization
5.4: Eigenvectors and Linear Transformations



5.1
5.2
5.3
5.4-6

5.1
5.2
5.3
5.4-6

5.1
5.2
5.3: video 1 and 2
5.4-6: none

5.1
5.2
5.3
5.4-6 - none

Chapter 6: Orthogonality and Least Squares

6.1: Inner Product, Length, & Orthogonality
6.2: Orthogonal Sets
6.3 & 6.4: Orthogonal Projections & Gram-Schmidt
6.5 & 6.6: Least-Squares Problems

6.1
6.2
6.3 & 6.4
6.5 & 6.6

6.1
6.2
6.3 & 6.4
6.5 & 6.6

6.1
6.2
6.3/4
6.5/6

6.1
6.2
6.3
6.4
6.5 and 6.6
Proofs in the notes/video (here)