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.
This week
☛ Monday ☚
Gram-Schmidt.
Homework due Monday
  • Reading: Lecture notes.
  • 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
  • Reading: Lecture notes.
☛ Friday ☚
Thanksgiving break. No class today, and no homework due.

Previous classes

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: H1F (tex file: H1F.tex, solutions: H1Fsol).


Week 2
☛ Monday ☚
No class: Labor Day

☛ Wednesday ☚
Subspaces and spanning sets.
Homework due Wednesday
☛ Friday ☚
Linear independence.
Homework due Friday
Week 3
☛ Monday ☚
Linear independence.
Homework due Monday
☛ Wednesday ☚
Bases.
Homework due Wednesday
☛ Friday ☚
Dimension.
Homework due Friday
Week 4
☛ Monday ☚
Row rank = column rank; dimension of solution space.
Homework due Monday
☛ Wednesday ☚
Linear transformations.
Homework due Wednesday
☛ Friday ☚
Range space and null space.
Homework due Friday
Week 5
☛ Monday ☚
Isomorphisms.
Homework due Monday
☛ Wednesday ☚
Lines, planes, and hyperplanes: equations and parametrizations.
Homework due Wednesday
☛ Friday ☚
Matrices.
Homework due Friday
Week 6
☛ Monday ☚
The ring of square matrices. Matrix inversion.
Homework due Monday
☛ Wednesday ☚
Matrices and linear transformations.
Homework due Wednesday
☛ Friday ☚
Matrices and linear transformations.
Homework due Friday
Week 7
☛ Monday ☚
Matrices and linear transformations: examples. Change of basis.
Homework due Monday
☛ 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
☛ Friday ☚
Determinants.
Homework due Friday
Week 8
☛ Monday ☚
\(\det(A)=\det(A^t)\).
Homework due Monday
☛ 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
☛ Friday ☚
Finish permutation expansions. Laplace expansion. Existence and uniqueness of the determinant.
Homework due Friday
Week 9
☛ Monday ☚
The determinant and volume.
Homework due Monday
☛ Wednesday ☚
Eigenvalues.
Homework due Wednesday
☛ Friday ☚
Eigenvalues, continued.
Homework due Friday
Week 10
☛ Monday ☚
Diagonalization.
Homework due Monday
☛ Wednesday ☚
Algebraic and geometric multiplicity. Jordan form.
Homework due Wednesday
☛ Friday ☚
Counting walks in graphs.
Homework due Friday
Week 11
☛ Monday ☚
Differential equations.
Homework due Monday
☛ Wednesday ☚
Inner products.
Homework due Wednesday
☛ Friday ☚
Length, distance, components, projections, angles.
Homework due Friday