Math 201

Fall 2019, Sections 01 and 02
Instructor: David Perkinson (schedule)
General info: Course description, office hours, grading, etc.
Text: Linear Algebra, by Jim Hefferon
Handouts: mathematical writing
LaTeX: getting started and LaTeX files for daily lectures
Sage: getting started
Math 201 study sessions: Monday and Thursday, 7–8 pm, ETC 205 and 208.
General drop-in tutoring: SMTWTh, 7–9 pm, L207. (No Sunday session during the first week.)

Midterm 1: solutions.
Midterm 2: There will be a second midterm after we cover determinants (probably due at the end of the 9th week).
Week 7
☛ Monday ☚
Change of basis.
Homework due Monday
  • Reading: Chapter Three, V.1 and V.2.
  • Practice problems: V.1: 1.7, 1.9, 1.10; V.2: 2.15, 2.16.
  • Turn in by 2 pm on Tuesday in the folder outside my office: H07T (tex file: H07T.tex).
☛ Wednesday ☚
Determinants.
Note: Substitute the following definition of the determinant for the one given in the book: determinant. (The definition given in the book does not work in a field where 1+1=0.)
Homework due Wednesday
  • Reading: Chapter Four, I.1 and I.2.
  • Practice problems: I.1: 1.1, 1.2, 1.3.
☛ Friday ☚
The determinant of the transpose of a matrix.
Homework due Friday
  • Reading: Chapter Four, I.1 and I.2.
  • Practice problems: I.1: 1.6, 1.7, 1.8, 1.9.
  • Turn in: H07F (tex file: H07F.tex).

Previous classes

Week 1
☛ Wednesday ☚
Solving systems of linear equations.
Homework due Wednesday
  • Reading: Chapter One, Sections I and III.
  • Practice problems: Chapter One, Section I: 1.17, 1.22, 1.27, 1.37 (challenge). (Note: do not turn in practice problems.)
☛ Friday ☚
Reduced row echelon form. Wikipedia link: Gaussian elimination.
Homework due Friday
  • Reading: Chapter One, Sections I and III.
  • Practice problems: Chapter One, Section I: 2.18, 2.21, 2.24, 2.29, 2.32 (challenge), 3.15, 3.18, 3.25; Section III: 1.8, 1.10, 1.14, 1.15, 2.11, 2.20, 2.24. (Note: do not turn in practice problems.)
Week 2
☛ Monday ☚
Vector spaces.
Homework due Monday
  • Reading: Chapter One, Section II.1, Chapter Two, Section I.
  • Practice problems: Chapter Two: 1.18, 1.19, 1.22, 1.28, 1.29, 2.20, 2.21, 2.26, 2.29, 2.44.
  • Turn in by 1 pm on Tuesday in the folder outside my office: H02T (tex file: H02T.tex, solutions: H02Tsol).
☛ Wednesday ☚
Subspaces and spanning sets.
Homework due Wednesday
  • Reading: Chapter Two, Section I.2.
  • Practice problems: Chapter Two, Section I.1: 1.18, 1.19, 1.22, 1.29, 1.30.
☛ Friday ☚
Linear independence.
Homework due Friday
  • Reading: Chapter Two, Section II.1.
  • Practice problems: Chapter Two, Section II.1: 1.20, 1.21, 1.23 (b).
  • Turn in: H02F (tex file: H02F.tex solutions: H02Fsol).
Week 3
☛ Monday ☚
Linear independence.
Homework due Monday
  • Reading: Same as last Friday: Chapter Two, Section II.1.
  • Practice problems: Same as last Friday: Chapter Two, Section II.1: 1.20, 1.21, 1.23 (b).
  • Turn in by 1 pm on Tuesday in the folder outside my office: H03T (tex file: H03T.tex solutions: H03Tsol).
☛ Wednesday ☚
Bases. (Supplement: here is a nice article on infinite-dimensional vector spaces.)
Homework due Wednesday
  • Reading: Chapter Two, III.1.
  • Practice problems: Chapter Two, III.1: 18, 19, 20, 21, 23, 29.
☛ Friday ☚
Dimension.
Homework due Friday
  • Reading: Chapter Two, III.2.
  • Practice problems: Chapter Two, III.2: 16, 18, 22, 26, 27, 34.
  • Turn in: H03F (tex file: H03F.tex, solutions: H03Fsol).
Week 4
☛ Monday ☚
Row space and column space
Homework due Monday
  • Reading: Chapter Two, III.3.
  • Practice problems: 3.17, 3.20, 3.21, 3.23, 3.29.
  • Turn in by 2 pm on Tuesday in the folder outside my office: H04T (tex file: H04T.tex, solutions: H04Tsol).
☛ Wednesday ☚
Linear transformations.
Homework due Wednesday
  • Reading: Chapter Three, II.1.
  • Practice problems: Chapter Three, II.1, 1.18, 1.19, 1.22, 1.26, 1.28, 1.32, 1.35, 1.37.
☛ Friday ☚
Range space and nullspace. Rank-nullity theorem.
Homework due Friday
  • Reading: Chapter Three, I.1, I.2, II.2.
  • Practice problems: Chapter Three, Section II: 2.21, 2.23, 2.24, 2.26, 2.35, 2.37, 2.40.
  • Turn in: Midterm 1 due at the beginning of class. To review for the midterm, please read through all of the lecture notes up through and including Monday of this week, and review the homework problems given up through last Friday—the solutions are available through Moodle. The midterm is closed-book/computers/etc. You should not consult others about your solutions. You have two hours to complete it once you have started. Comments: Please be particularly sure you can solve systems of linear equations as we have presented it. That means knowing precisely what constitutes reduced echelon form and after computing it, being able to express your solution exactly in the two forms presented in the lecture on Friday of Week 1.
    Midterm 1 solutions
Week 5
☛ Monday ☚
Isomorphisms.
Homework due Monday
  • Reading: Chapter Three, Sections I.1, I.2, II.2.
  • Practice problems: Chapter Three, Section I: 1.21, 1.23, 1.30, 1.37, 2.15, 2.19.
  • Turn in by 2 pm on Tuesday in the folder outside my office: H05T (tex file: H05T.tex, solutions: H05Tsol).
☛ Wednesday ☚
Lines, planes, and hyperplanes: equations and parametrizations.
Homework due Wednesday
  • Reading: Chapter One, II.1
  • Practice problems: Chapter One, II.1: 1, 2, 3, 4, 5, 6.
☛ Friday ☚
Matrices.
Homework due Friday
  • Reading: Chapter Four, IV.1 and IV.2.
  • Practice problems: IV.1: 1.8, 1.11; IV.2: 2.14, 2.15, 2.16.
  • Turn in: H05F (tex file: H05F.tex, solutions: H05Fsol ).
Week 6
☛ Monday ☚
Matrix inversion.
Homework due Monday
  • Reading: Chapter 3, IV.4.
  • Practice problems: Chapter 3, IV.4: 4.15,Chapter 3, IV.4: 4, 17, 18, 20, 22, 28, 33, 35,
  • Turn in by 2 pm on Tuesday in the folder outside my office: H06T (tex file: H06T.tex solutions: H06Tsol).
☛ Wednesday ☚
Matrices and linear transformations.
Homework due Wednesday
  • Reading: Chapter Three, III.2.
  • Practice problems: 2.12, 2.15.
☛ Friday ☚
Matrices and linear transformations.
Homework due Friday
  • Reading: Chapter Three, III.2.
  • Practice problems: 2.12, 2.15.
  • Turn in: H06F (tex file: H06F.tex).
Week 7
☛ Monday ☚
Change of basis.
Homework due Monday
  • Reading: Chapter Three, V.1 and V.2.
  • Practice problems: V.1: 1.7, 1.9, 1.10; V.2: 2.15, 2.16.
  • Turn in by 2 pm on Tuesday in the folder outside my office: H07T (tex file: H07T.tex).
☛ Wednesday ☚
Determinants.
Note: Substitute the following definition of the determinant for the one given in the book: determinant. (The definition given in the book does not work in a field where 1+1=0.)
Homework due Wednesday
  • Reading: Chapter Four, I.1 and I.2.
  • Practice problems: I.1: 1.1, 1.2, 1.3.
☛ Friday ☚
The determinant of the transpose of a matrix.
Homework due Friday
  • Reading: Chapter Four, I.1 and I.2.
  • Practice problems: I.1: 1.6, 1.7, 1.8, 1.9.
  • Turn in: H07F (tex file: H07F.tex).