PLEASE REFRESH THE PAGE AT EACH VISIT!

Welcome to Math 3333: Linear Algebra I, this Fall 2020! Today is Thursday, March 13, 2025.

Links to lecture videos and notes

See also OU Calendar for Fall 2020 for important deadlines and other dates.

Lecture Videos

List of all lecture videos

(Credit: Slides were originally written by Greg Muller and Karen Seyffarth, used with thanks)

---

Finals Week (Dec 14 – 18)

Wed, Dec 16 at 10:30am to 12:30pm

---

Past: Week 16 Exams Prep Week (Sun, Dec 6 – Sun, Dec 13)

---

Past: Week 15 (Nov 30 – Dec 4)

• Mon Watch and read notes Lecture 17a bases and dimensions for vector spaces, part a; linear independence and spanning for general vector spaces; dimension is the number elements in any basis of a vector space; standard basis for other vector spaces

• Wed Watch and read notes Lecture 17b bases and dimensions for vector spaces, part b; every spanning set contains a basis; 2 out of 3 rule; coefficient vector; from smooth functions back to vectors

• Fri In-class quiz

• Due Mon December 7 on Gradescope at noon: Week 14/15 Worksheet (individual)

---

Past: Week 14 (Nov 14 – 27)

• Mon Watch and read notes Lecture 16b vector spaces (subspaces); a subspace is a vector space is always a vector space; the set of solutions to a linear differential equation is always a vector space; examples for showing that a subset of a vector space is a subspace or not a subspace

• Wed no class (Thanksgiving break)
• Fri no class (Thanksgiving break)

---

Past: Week 13 (Nov 16 – 20)

• Mon Watch and read notes Lecture 15b Eigenbases (finding eigenbases); determine whether a matrix has an eigenbasis without following the algorithm; A matrix with n distinct eigenvalues must have an eigenbasis
  • Mon during class, continue learning the materials for presentation
• Wed Watch and read notes Lecture 15c Eigenbases (diagonalization); how to diagonalize a matrix with an eigenbasis; speed up multiplication with diagonalization; The spectral theorem: a matrix is symmetric iff it has an orthogonal eigenbasis
  • Wed during class, continue learning the materials for presentation
  • Poll about class activity for Mon after break
• Fri Watch and read notes Lecture 16a Vector spaces; definition and axioms; addition, scalar multiplication, and linear combinations for vector space of polynomials

Friday, November 20 is the last day to do an automatic drop for a grade of W via One. Withdrawals this semester will not count toward the overall limit of five withdrawals during a student’s course of study at the university.

(After November 20, petition to the Dean of the student’s College is required.)

Add and Drop a Class page

Registrar’s Calendar

---

Past: Week 12 (Nov 9 – 13)

• Mon Watch and read notes lecture 14a Basis algorithm for the kernel of a matrix; basis algorithm for the eigenspace of a matrix; dimension of the kernel of a matrix is matrix’ width minus matrix’ rank
  • In-class practice quiz activity (very small extra credit points)
• Wed Watch and read notes lecture 14b Rank and dimensions (without row reduce); finding rank of a matrix, finding dimension of the kernel of a matrix, finding dimension of the image of a matrix without row reduce; Rank-nullity theorem; Inequalities of ranks for product of matrices
  • Wed in-class quiz
• Fri Watch and read notes Lecture 15a Eigenbases; definition of an eigenbasis for a matrix; how to check when a set is an eigenbasis for a matrix
  • Fri during class, start learning the materials for presentation
• (No wksheet due this coming Monday, Week 13)

---

Past: Week 11 (Nov 2 – 6)

• Mon Watch and read notes lecture 13a bases; showing that a set is a basis for the n-D space using rank, determinant, invertibility; definition of dimension of a subspace
• Fri Watch and read notes lecture 13b bases (basis computations and dimensions); finding a basis for the image of matrix; starting from a spanning set, quickly find a basis by throwing out vectors; given the dimension of a subspace, determining whether a set is a basis just by checking linear independence
  • There were new examples from the live lecture on Friday (see notes attached to lecture 13b, titled Exercise 9 and Exercise 10)
• Due Mon November 9 on Gradescope: Week 11 Worksheet (individual)

---

Past: Week 10 (Oct 26 – 30)

• Mon Watch or read notes lecture 12a Spanning sets, showing that a set of vectors spans a subspace
• Wed No new lecture (campus is closed)

• Fri Watch and read notes lecture 12b Linear independence, a basis is a linearly independent spanning set

• Due Mon November 2 Friday, Nov 6 on Gradescope: Week 9/10 Worksheet (individual homework!)

---

Past: Week 9 (Oct 19 – 23)

• Mon Watch or read notes lecture 10b Linear transformations, part b (Finding the matrix of linear transformation using standard basis vectors; geometric meaning of matrix algebra, determinant, and eigenvectors)
• Wed Watch or read notes lecture 11a Subspaces (solution set of a homogeneous solution, def of subspace, kernel of a matrix, eigenspace, image of a matrix)
  • Wed live session: Presented extra example problems: Extra problems from lecture 9a, 9b, 10a, 10b, and solving linear system
• Fri Watch or read notes lecture 11b Subspaces, how to prove a subset is not a subspace/ prove a subset is a subspace

---

Past: Week 8 (Oct 12 – 16)

• Mon no new lecture video
• Wed Watch or read notes lecture 10a Linear transformations (preserves addition, scalar multiplication, linear combinations)
• Fri no new lecture video

MIDTERM slots during week 7 and 8

• Due Mon October 19 on Gradescope: Week 7/8 Worksheet (individual homework!)

---

Past: Week 7 (Oct 5 – 9)

• Mon Watch or read notes lecture 9b Vector geometry with matrices
• No new lecture Wed and Fri

MIDTERM slots during week 7 and 8

---

Past: Week 6 (Sep 28 – Oct 2)

• Mon Watch or read notes lecture 8a Characteristic polynomials (given a square matrix, find all eigenvalues)
• Wed Watch or read notes lecture 8b Characteristic polynomials
• Fri Watch or read notes lecture 9a Vector geometry (intro)

Due the Mon after week 6 (at noon): Week 6 presentation slides and recording

• Suggested practice for lecture 8a (finding eigenvalues): Section 3.3 Exercises 1(b,d,f,h) and 3. In Exercise 3.31, you don’t need to find the matrix P.

• Suggested practice for lecture 8b (characteristic polynomials): TBA

---

Past: Week 5 (Sep 21 – 25)

• Mon Watch or read notes lecture 6b Determinants, second part
• Wed Watch or read notes lecture 7a cofactors (and how they relate to determinants and inverses)

• Fri Watch or read notes lecture 7b eigenvectors (given a number lambda, find all eigenvectors associated with lambda)

• Suggested practice for lecture 6 (check with solution manual and calculator): Section 3.1, Exercise 5 Section 3.2, Exercises 2(b,d,f), 6(b)

• Suggested practice for lecture 7a (cofactors): Section 3.1 (The Cofactor expansion, pg 156), Exercise 1(b,d,f,h,j,l,n,p) and 26

• Suggested practice for lecture 7b (eigenvectors): None yet

• In-class quiz on Wed
• Due Mon Sep 28: Week 5 Worksheet

---

Past: Week 4 (Sep 14 – 18)

• Mon Watch or read notes lecture 5a Matrix inverses
• Wed Watch or read notes lecture 5b Matrix inverse: algorithm

• Fri Watch or read notes lecture 6a Determinants

• Suggested practice for lecture 5: Section 2.4 (inverses), pg 91-92, 94 Exercises 1, 4, 6, and 28

Due Mon Sep 21: Week 4 presentation slides and recording

---

Past: Week 3 (Sep 7 – 11)

• Mon Labor Day (no class, no new lecture)
• Wed Watch or read notes lecture 4a Matrix multiplication

• Fri Watch or read notes lecture 4b Matrix multiplication (properties of matrix arithmetic)

• Suggested practice for lecture 4 (see Student Solution Manual): Section 2.3, pg 77-78 Exercises 3, 6, 16

Due Mon Sept 14: Week 2 and 3 Worksheet

---

Past: Week 2 (Aug 31 – Sep 4)

• Mon Watch or read notes lecture 2b Gaussian elimination (rank, homogeneous system)
• Wed Watch or read notes lecture 3a Matrices and Vectors (addition, scalar multiplication, linear combination, transpose)

• Fri Watch or read notes lecture 3b Matrices and Vectors (zero matrix, identity matrix, matrix to vector multiplication)

• Suggested practice for lecture 2 (see Student Solution Manual):
  • Section 1.1, pg 8-9, Exercises 7, 9, 11, and 14
  • Section 1.2, pg 17-19, Exercises 3, 7, and 16
• Suggested practice for lecture 3 (see Student Solution Manual):
  • Section 2.1, pg 44, Exercises 2, 3, 8, and 16. (A matrix is called symmetric if it is equal to its transpose)
  • Section 2.2, pg 62-63 Exercises 2 and 10

---

Past: Week 1 (Aug 24 – 28)

• Mon Watch or read notes lecture 1a Systems of linear equations
• Wed Watch or read notes lecture 1b Systems of linear equations (con’t)
• Fri Watch or read notes lecture 2a Gaussian elimination

Due Sun Aug 30: Week 1 Worksheet