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Math 220: Linear Algebra

Spring 2024

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 (40:04)
1.2 (38:35)
1.3 (42:45)
1.4 (43:32)
1.5 (44:05)
1.7 (58:58)
1.8 (39:30)
1.9 (1:02:55)

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 (46:08)
2.2 (37:22)
2.3 (27:11)

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 (1:13:03)

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 (1:02:15)
4.2 (57:13)
4.3: (1:19:40)
4.4 (1:21:40)
4.5 (1:37:16)
4.6 (1:12:26)

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 (59:50)
5.2 (39:54)
5.3: (59:36)
5.4-6: In three parts
part 1 (33:27)
part 2 (24:51)
part 3 (59:37)

5.1
5.2
5.3
5.4-6

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 (1:04:36)
6.2 (1:25:39)
6.3/4 (1:08:30)
6.5/6 (1:20:18)

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