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Math 201, Fall 2022
Linear Algebra

 

The main website for this course appeared on Moodle. Here is a summary of the content of Math 201 for Fall 2022.

 

Syllabus

 

Week 1

Lecture 1, Lecture 2

• Topics: Solving systems of linear equations, matrices, reduced row echelon form, olution sets, equivalence relations, geometry of vectors in R2 and R3.
• Reading: Syllabus, Chapter One, Sections I, II.1, and III.
• Practice problems:
  Chapter One
  Section I: 1.17, 1.22, 1.27, 1.37 (challenge); 2.18.
  Section III: 1.8, 1.10, 1.14
  Section I: 2.21, 2.24, 2.29, 2.31 (challenge); 3.15, 3.18, 3.25.
  Section II: 1.3, 1.5, 1.7, 1.8.
  Section III: 1.15, 2.11, 2.20, 2.24.

Week 2

Lecture 3, Lecture 4

• Topics: Vector spaces and fields. Properties of vector spaces, subspaces, linear combinations, and spans
• Reading: Chapter Two, Section I
• Practice problems:
  Chapter Two, Section I: 1.18, 1.19, 1.22, 1.28, 1.29, 1.40, 2.20, 2.21.
  Chapter Two, Section I.2: 2.26, 2.29, 2.36, 2.44, 2.47
  

Week 3

Lecture 5, Lecture 6

• Topics: Linear independence, bases, dimension.
• Reading: Chapter Two, Sections II.1, III.1, III.2
• Practice problems:
  Chapter Two, Section II: 1.23 (c), 1.28, 1.29, 1.33 (ab); Section III: 1.20, 1.21
  Chapter Two, Section III: 1.23, 1.25, 1.31 (a); 2.15, 2.17, 2.21.

Week 4

Lecture 7, Lecture 8

• Topics: More on dimension, row and column space of a matrix, rank, linear transformations (aka homomorphisms).
• Reading: Chapter Two, Sections III.2, III.3
• Practice problems:
  Chapter Two, Section II: 2.25, 2.26, 2.33; 3.18, 3.22
  Chapter Two, Section III: 3.17, 3.20, 3.21, 3.23, 3.29.

Week 5

Lecture 9, Lecture 10

• Topics: Range and null space, rank-nullity theorem, linear extensions
• Reading: Chapter Three, Sections I.1&2, II.1&2
• Practice problems:
  Chapter Three
  Section II: 1.19, 1.20, 1.25, 1.28, 1.34, 1.36; 2.21, 2.23, 2.24, 2.26, 2.35, 2.37, 2.40
  Section I: 2.15, 2.19, 2.20
  

Week 6

Lecture 11, Lecture 12

• Topics: Isomorphisms, dot product, matrices as linear maps, matrices representing linear transformations and their properties
• Reading: Chapter Three, Sections I.1&2, III.1&2
• Practice problems:
  Chapter Three
  Section I: 2.21, 1.23, 1.30, 1.37
  Section III: 1.16, 1.17, 1.27(a)(b)
  Section III: 1.21, 1.27 (c)(d), 2.12, 2.13, 2.15, 2.22, 2.26, 2.29, 2.33

Week 7

Lecture 13, Lecture 13/14 exercises, Lecture 14

• Topics: Matrix multiplication, the identity matrix, inverse of a matrix
• Reading: Chapter Three, Sections IV.2, IV.3, IV.4
• Practice problems:
  Chapter Three
  Section IV.2: 14, 17, 26, 28, 33
  Section IV.3: 3.44
  Section IV.3: 24, 25, 30, 38, 40, 51(a)-(d)
  Section IV.4: 15, 18, 20, 22, 28, 33

Week 8

Lecture 15, Lecture 16

• Topics: Review, change of basis, determinants: definition and some properties
• Reading: Chapter Three, Section V.2; Chapter Four, Sections I.1 and I.2
• Practice problems:
  Chapter Three, Section V: 2.13, 2.15, 2.31
  Chapter Four, Section I: 2.8, 2.11, 2.12, 2.15, 2.18, 2.22

Week 9

Lecture 17 worksheet, Lecture 18

• Topics: Determinants: more properties, existence, permutation and Laplace expansions of the determinant
• Reading: Chapter Four, Sections I.2&3, III
• Practice problems:
  Chapter Four
  Section I: 2.8, 2.11, 2.12, 2.15, 2.18, 2.22
  Section I: 3.18, 3.21, 3.24, 3.27, 3.36
  Section III: 1.14, 1.28, 1.29

Week 10

Lecture 19, Lecture 20

• Topics: Eigenvalues, eigenvectors, eigenspaces, diagonalizability, Jordan form
• Reading: Chapter Five, Sections II.1, II.2 and II.3
• Practice problems:
  Chapter Five
  Section II: 1.6, 1.8, 1.13, 1.15, 1.17; 2.8, 2.11; 3.21, 3.22, 3.26, 3.29, 3.42.
  Section II.3: 3.24, 3.25, 3.28, 3.29

Week 11

Lecture 21, Lecture 22

• Topics: Inner product spaces, Gram-Schmidt orthogonalization
• Reading: Chapter One, Section II.2, Inner product spaces, Chapter Three, Section VI.2, Gram-Schmidt orthogonalization

Week 12

Lecture 23

• Topics: Orthogonal complements and projections

Week 13

Lecture 24

• Topics: Spectral theorem

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