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

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)

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Finals Week (Dec 14 – 18)

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

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

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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)

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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)

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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

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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)

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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)

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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!)

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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

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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!)

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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

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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

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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

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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

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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

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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

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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