MATH 2331, Section 6 — Linear Algebra

Course description: Welcome to MATH 2331. This course introduces basic concepts, algorithms, theory, and applications of linear algebra.

Text book: Linear Algebra with Applications, (5th ed.), O. Bretscher, Pearson Prentice Hall.

Syllabus: pdf 

Homeworks:

  • Homework 1 : pdf | Due 09/14/2023

  • Homework 2: pdf | Due 09/21/2023

  • Homework 3: pdf | Due 09/28/2023

  • Homework 4: pdf | Due 10/12/2023

  • Homework 5: pdf | Due 10/19/2023

  • Homework 6: pdf | Due 10/26/2023

  • Homework 7: pdf | Due 11/02/2023

  • Homework 8: pdf | Due 11/16/2023

  • Homework 9: pdf | Due 11/27/2023

Midterms:

  • Midterm 1: in-class 10/02/2023 | Lectures 1-10 | Homeworks 1-3

  • Midterm 2: in-class 11/02/2023 | Lectures 10-20 | Homeworks 4-6

  • Midterm 3: in-class 11/30/2023 | Lectures 20-28 | Homeworks 7-9

Final Exam:

  • 12/14/2023 | 10:30 AM - 12:20 PM | 128 Forsyth | Old finals: zip

Lectures:

  • Lecture 1 [09/06/2023] pdf: Intro to linear equations and systems of linear equations (Chapter 1.1)

  • Lecture 2 [09/07/2023] pdf: Matrices, elementary row operations, Gauss-Jordan elimination, the rref of a matrix (Ch 1.2)

  • Lecture 3 [09/11/2023] pdf: The set of solutions of a linear system, the rank of a matrix (Ch 1.3)

  • Lecture 4 [09/13/2023] pdf: Matrix-vector multiplication, linear combinations, dot product (Ch. 1.3)

  • Lecture 5 [09/14/2023] pdf: Linear transformations, the matrix of a linear transformation (Ch. 2.1)

  • Lecture 6 [09/18/2023] pdf: The inverse of a linear transformation, orthogonal projections (Ch 2.2)

  • Lecture 7 [09/20/2023] pdf: Geometric linear transformations (Ch. 2.3)

  • Lecture 8 [09/21/2023] pdf: Matrix multiplication and computing inverses (Ch 2.3, 2.4)

  • Lecture 9 [09/25/2023] pdf: The kernel and the image of a linear transformation (Ch 3.1)

  • Lecture 10 [09/27/2023] pdf: Computing the kernel and image, examples and properties (Ch 3.1)

  • Lecture 11 [10/04/2023] pdf: Linear subspaces of R^n, Spans (Ch 3.2)

  • Lecture 12 [10/05/2023] pdf: Linear independence, Bases (Ch 3.2)

  • Lecture 13 [10/11/2023] pdf: Finding bases for the image and kernel, dimension, rank-nullity theorem (Ch 3.3)

  • Lecture 14 [10/12/2023] pdf: Consequences of the rank-nullity theorem, coordinates with respect to a basis (Ch 3.4)

  • Lecture 15 [10/16/2023] pdf: The B-matrix of a linear transformation (Ch 3.4)

  • Lecture 16 [10/18/2023] pdf: The standard matrix vs the B-matrix, similar matrices (Ch 3.4)

  • Lecture 17 [10/19/2023] pdf: Orthonormal bases (Ch 5.1)

  • Lecture 18 [10/23/2023] pdf: Orthogonal projections and orthogonal complements (Ch 5.1)

  • Lecture 19 [10/25/2023] pdf: Finding bases for the orthogonal complement, Gram-Schmidt, QR decomposition (Ch 5.2)

  • Lecture 20 [10/26/2023] pdf: Computing the QR decomposition, Orthogonal matrices (Ch 5.2 and 5.3)

  • Lecture 21 [11/06/2023] pdf: Properties of the transpose, Least Squares (Ch 5.4)

  • Lecture 22 [11/08/2023] pdf: Computing solutions to least-squares problems, determinants revisited (Ch 5.4, 6.1, 6.2)

  • Lecture 23 [11/09/2023] pdf: The determinant of 3x3 matrices (Ch 6.2, 6.3)

  • Lecture 24 [11/13/2023] pdf: Laplace expansions, algebraic properties of the determinant (Ch 6.2, 6.3)

  • Lecture 25 [11/15/2023] pdf: Elementary row operations and the determinant, Eigenvalues and eigenvectors (Ch 6.2, 7.1)

  • Lecture 26 [11/16/2023] pdf: Finding the eigenvalues of a matrix, algebraic multiplicity (Ch 7.2)

  • Lecture 27 [11/20/2023] pdf: Eigenvectors, eigenspaces and diagonalization (Ch 7.3)

  • Lecture 28 [11/27/2023] pdf: Orthogonal diagonalization, the spectral theorem (Ch. 8.1)

  • Lecture 29 [11/29/2023] pdf: The spectral theorem, computing orthogonal diagonalizations (Ch 8.1)

  • Lecture 30 [12/04/2023] pdf: Singular Value Decomposition (Ch. 8.3)

  • Lecture 31 [12/06/2023] pdf: Computing the SVD (Ch. 8.3)