### Math 201

Spring 2017, 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; Sage: getting started
Math 201 study sessions: Monday and Thursday nights, 7–8pm, L204.
General drop-in tutoring: SMTWTh, 7–9 pm, L389.

Midterm 1: solutions.
Midterm 2: review sheet, solutions.
Final exam: The final exam with be a 3-hour take-home exam. It will be available for pick-up at noon on Monday, December 11 and will be due on Thursday, December 14 by 5pm. Review session 7–9 pm Sunday, December 10, L204. Here are some practice problems, and solutions.
Collected lecture notes, homework, and handouts: : Math 201,
Week 1
☛ Monday ☚
Solving systems of linear equations.
Homework due Monday
• Reading: Chapter One, Sections I and III.
• Practice problems: Chapter One, Section I: 1.17, 1.22, 1.27, 1.37 (challenge).
☛ Wednesday ☚
Reduced row echelon form. Wikipedia link: Gaussian elmination.
Homework due Wednesday
• 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.
☛ Friday ☚
Vector spaces.
Homework due Friday
• 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: H01F (tex file: H01F.tex, solutions: H01Fsol).

Week 2
☛ Monday ☚
No class: Labor Day

☛ 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.
• Turn in at the beginning of class today: H02T (tex file: H02T.tex, solutions: H02Tsol ).
Here are some examples demonstrating the correct style for a solution to the second problem in the above homework: supplement.
☛ 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 2 pm on Tuesday in the folder outside my office: H03T (tex file: H03T.tex, solutions: H03Tsol).
☛ Wednesday ☚
Bases.
Homework due Wednesday
• Practice problems: Chapter Two, III.1: 18, 19, 20, 21, 23, 29.
☛ Friday ☚
Dimension.
Homework due Friday
• 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 rank = column rank; dimension of solution space.
Homework due Monday
• 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
• 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 null space.
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 last Monday's, and review the homework problems given up through last Friday—the solutions are available through our 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.
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: H05Fsol).
☛ Wednesday ☚
Lines, planes, and hyperplanes: equations and parametrizations.
Homework due Wednesday
• 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 ☚
The ring of square matrices. Matrix inversion.
Homework due Monday
• 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
• Practice problems: 2.12, 2.15.
☛ Friday ☚
Matrices and linear transformations.
Homework due Friday
• Practice problems: 2.12, 2.15.
• Turn in: H06F (tex file: H06F.tex, solutions: H06Fsol).
Week 7
☛ Monday ☚
Matrices and linear transformations: examples. 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 solutions: H07Tsol).
☛ 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 ☚
Determinants.
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 solutions: H07Fsol.)
Week 8
☛ Monday ☚
$$\det(A)=\det(A^t)$$.
Homework due Monday
• Reading: Chapter 3, end of IV. (elementary matrices).
• Practice problems: None.
• Turn in by 2 pm on Tuesday in the folder outside my office: H08T (tex file: H08T.tex solutions: H08Tsol).
☛ Wednesday ☚
Permutation expansion of the determinant.
Note: We will have a second midterm, handed out next Wednesday, then collected in class the following Friday. It will cover everything we have done up through and including determinants.
Homework due Wednesday
• Practice problems: Chapter Four, I.3: 3.20, 3.21.
☛ Friday ☚
Finish permutation expansions. Laplace expansion. Existence and uniqueness of the determinant.
Homework due Friday
• Practice problems: Chapter 4, III.1: 1.14
• Turn in: H08F (tex file: H08F.tex solutions: H08Fsol).
Week 9
☛ Monday ☚
Geometric interpretation of the determinant.
Homework due Monday
• Practice problems: None.
• Turn in by 2 pm on Tuesday in the folder outside my office: H09T (tex file: H09T.tex solutions: H09Tsol).
☛ Wednesday ☚
Eigenvalues.
Homework due Wednesday
• Practice problems: 3.21, 3.22, 3.23.
☛ Friday ☚
Eigenvalues, continued.
Homework due Friday
• Practice problems: 3.21, 3.22, 3.23.
• Turn in: Midterm 2. Solutions.
Week 10
☛ Monday ☚
Diagonalization.
Homework due Monday
• Practice problems: 3.24, 3.25, 3.28, 3.29.
• Turn in by 2 pm on Tuesday in the folder outside my office: H10T (tex file: H10T.tex solutions: H10Tsol).
☛ Wednesday ☚
Algebraic and geometric multiplicity. Jordan form.
Homework due Wednesday
• Practice problems: None.
☛ Friday ☚
Counting walks in graphs.
Homework due Friday
• Practice problems: None.
• Turn in: H10F (tex file: H10F.tex solutions: H10Fsol).
Week 11
☛ Monday ☚
Differential equations.
Homework due Monday
• Practice problems: None.
• Turn in by 2 pm on Tuesday in the folder outside my office: H11T (tex file: H11T.tex solutions: H11Tsol).
☛ Wednesday ☚
Inner products.
Homework due Wednesday
• Practice problems: Notes.
☛ Friday ☚
Length, distance, components, projections, angles.
Homework due Friday
• Practice problems: None.
• Turn in: H11F (tex file: H11F.tex solutions: H11Fsol).
Week 12
☛ Monday ☚
Gram-Schmidt.
Homework due Monday
• Turn in by 2 pm on Tuesday in the folder outside my office: H12T (tex file: H12T.tex solutions: H12Tsol).
☛ Wednesday ☚
Orthogonal complements and orthogonal projections.
Homework due Wednesday
☛ Friday ☚
Thanksgiving break. No class today, and no homework due.

Week 13
☛ Monday ☚
Least squares.
Homework due Monday
• Turn in by 2 pm on Tuesday in the folder outside my office: H13T (tex file: H13T.tex solutions: H13Tsol).
☛ Wednesday ☚
Markov chains I.
Homework due Wednesday
☛ Friday ☚
Markov chains II. Pagerank I.
Homework due Friday
Week 14
☛ Monday ☚
Pagerank II.
Homework due Monday
• Reading: Lecture notes and Pagerank.
• Turn in by 2 pm on Tuesday in the folder outside my office: H14T (tex file: H14T.tex solutions: H14Tsol.)
☛ Wednesday ☚
Pagerank III.
Homework due Wednesday