MATH 2331, Section 1 — Linear Algebra
Text book: Linear Algebra with Applications, (5th ed.), O. Bretscher, Pearson Prentice Hall.
Syllabus: pdf
Homework:
Homework 1: pdf | Due 01/18/2024
Homework 2: pdf | Due 01/25/2024
Homework 3: pdf | Due 02/01/2024
Homework 4: pdf | Due 02/15/2024
Homework 5: pdf | Due 02/22/2024
Homework 6: pdf | Due 02/29/2024
Homework 7: pdf | Due 03/12/2024
Homework 8: pdf | Due 03/28/2024
Homework 9: pdf | Due 04/04/2024
Homework 10: pdf | Due 04/17/2024
Midterms:
Midterm 1: 02/05/2024 | Lectures 1-10 | Homework 1-3
Midterm 2: 03/14/2024 | Lectures 10-20 | Homework 4-7
Midterm 3: 04/08/2024 | Lectures 20-27 | Homework 8-9
Final: 04/24/2024 | 10:30 AM - 12:30 PM | West Village H - Room 110 | Past final exams (pdfs)
Lectures:
Lecture 1 [01/08/2024] pdf: Intro to linear equations and systems of linear equations (Ch 1.1)
Lecture 2 [01/10/2024] pdf: Matrices, elementary row operations and the Reduced Row-Echelon Form - RREF (Ch 1.2)
Lecture 3 [01/11/2024] pdf: Number of solutions in a linear system, the rank of a matrix. (Ch 1.2 and 1.3)
Lecture 4 [01/17/2024] pdf: Vectors and general solutions to linear systems, matrix-vector multiplication, the matrix form of a linear system (Ch 1.2 and 1.3)
Lecture 5 [01/18/2024] pdf: Linear combinations, dot products, matrix-vector multiplication as dot products (Ch 1.3)
Lecture 6 [01/22/2024] pdf: Linear transformations, the matrix of a linear transformation (Ch 2.1)
Lecture 7 [01/24/2024] pdf: Geometric linear transformations — scaling, rotation, projection, reflection, shear (Ch 2.2)
Lecture 8 [01/25/2024] pdf: Matrix multiplication and compositions, the inverse of a bijective linear transformation (Ch 2.3 and 2.4)
Lecture 9 [01/29/2024] pdf: Computing the inverse of a bijective linear transformation (Ch 2.4)
Lecture 10 [01/31/2024] pdf: The image and kernel of a linear transformation/matrix (Ch 3.1)
Lecture 11 [02/08/2024] pdf: Linear subspaces, spans and linear independence (Ch 3.2)
Lecture 12 [02/12/2024] pdf: Bases for a linear subspace, dimension (Ch 3.2)
Lecture 13 [02/14/2024] pdf: Bases for the image and the kernel, dimension is well-defined (Ch 3.2)
Lecture 14 [02/15/2024] pdf: The rank-nullity theorem, coordinates with respect to a basis (Ch 3.3 and 3.4)
Lecture 15 [02/21/2024] pdf: Computing the coordinates of a vector, the B-matrix of a linear transformation (Ch 3.4)
Lecture 16 [02/22/2024] pdf: Computing the B-matrix, similar matrices (Ch 3.4)
Lecture 17 [02/26/2024] pdf: Orthonormal bases (Ch 5.1)
Lecture 18 [02/28/2024] pdf: Orthogonal projections and orthogonal complements (Ch 5.1)
Lecture 19 [02/29/2024] pdf: Computing bases for V^\perp, the Gram-Schmidt algorithm, the QR decomposition theorem (Ch 5.1 and 5.2)
Lecture 20 [03/11/2024] pdf: Computing the QR decomposition, orthogonal matrices (Ch 5.2 and 5.3)
Lecture 21 [03/18/2024] pdf: Properties of the transpose, Least squares and the normal equation (Ch 5.4)
Lecture 22 [03/20/2024] pdf: Computing solutions to least-squares problems, determinants revisited (Ch 5.4, 6.1, 6.2)
Lecture 23 [03/21/2024] pdf: The determinant of 3x3 matrices (Ch 6.2, 6.3)
Lecture 24 [03/25/2024] pdf: Laplace expansions, algebraic properties of the determinant (Ch 6.2, 6.3)
Lecture 25 [03/27/2024] pdf: Elementary row operations and the determinant, Eigenvalues and eigenvectors (Ch 6.2, 7.1)
Lecture 26 [03/28/2024] pdf: Finding the eigenvalues of a matrix, algebraic multiplicity (Ch 7.2)
Lecture 27 [04/01/2024] pdf: Eigenvectors, eigenspaces and diagonalization (Ch 7.3)
Lecture 28 [04/03/2024] pdf: More on diagonalization, orthogonal diagonalization (Ch. 7.3 and 8.1)
Lecture 29 [04/10/2024] pdf: The spectral theorem, computing orthogonal diagonalizations (Ch 8.1)
Lecture 30 [04/11/2024] pdf: The Singular Value Decomposition — SVD (Ch. 8.3)