Please see below for lecture summaries, homework and other study material.

Date	Topics
Jan.15.	Matrix encodings of linear systems. Elementary row operations on matrices. Notes.
Jan.18.	MLK Holiday; no class.
Jan.20.	Echelon and reduced echelon forms. Notes. Homework 1 (due Fri. Jan. 29): 1.1: 3, 8, 10, 12, 20; 1.2: 2, 4, 8, 12, 16.
Jan.22.	The Gaussian Elimination Algorithm. Notes.
Jan.25.	Solution sets of linear systems from echelon forms. Vectors and linear combinations. Notes.
Jan.27.	Matrix-vector products. Vector equations and matrix equations. Spans. Notes. Homework 2 (due Wed. Feb. 3): 1.3: 8, 10, 12, 18; 1.4: 4, 8, 12, 14.
Jan.29.	Spanning properties via Echelon forms. Notes.
Feb.01.	Linear independence: definition, examples and tests. Notes.
Feb.03.	Geometry of vectors. Homogeneous vs. non-homogeneous equations. Notes. Homework 3 (due Wed. Feb. 10): 1.4: 15, 16; 1.5: 4, 6, 13, 16, 18, 19, 32.
Feb.05.	Size bounds on spanning and linearly independent sets. Introduction to linear maps. Notes.
Feb.08.	Examples of linear and non-linear maps. Linear maps vs. matrix multiplication. Notes.
Feb.10.	Image, kernel, surjectivity and injectivity of linear maps. Notes. Homework 4 (due Thur. Feb. 18): 1.7: 4, 6, 8, 12, 20, 22, 31, 32; 1.8: 8, 10, 12, 14, 16.
Feb.12.	Geometric linear transformations of R^2. Midterm I date announced: March 1. Notes.
Feb.15.	Matrix addition, scaling and multiplication. Notes. Homework 5 (due Wed. Feb. 24): 1.9: 4, 6, 8, 14, 22, 38, 40; 2.1: 2, 6, 7, 9.
Feb.17.	Wellness Day; no class.
Feb.19.	Properties of matrix multiplication. Matrix products vs. composition of linear maps. Notes.
Feb.22.	Matrix powers and transposes. Inverse of matrices. Notes. Details and review problems on Midterm I.
Feb.24.	Invertibility vs. cancellation. Properties of matrix inverses. The invertible matrix theorem. Notes. Homework 6 (due Wed. Mar. 3): 2.1: 10, 12, 27; 2.2: 2, 4, 7, 8.
Feb.26.	More on the invertible matrix theorem. Review for Midterm I. Notes.
Mar.01.	More midterm review. Algorithm for testing invertibility and finding inverses. Notes. Midterm I (available on Canvas from 5:59 pm to 11:59 pm).
Mar.03.	Invertible linear maps. Subspaces of R^n. Notes. Homework 7 (due Wed. Mar. 10): 2.2: 13, 32; 2.3: 6, 33, 34; 2.8: 4, 8, 10, 12.
Mar.05.	Examples and non-examples of subspaces. Proofs on subspaces. Notes.
Mar.08.	Null spaces. Bases of subspaces of R^n. Notes.
Mar.10.	Dimension. Finding bases and dimension. The rank-nullity theorem. Notes. Homework 8 (due Wed. Mar. 17): 2.8: 14, 18, 20, 24, 38; 2.9: 2, 4, 8, 14.
Mar.12.	Coordinate systems. Computation of determinants. Notes.
Mar.15.	Class cancelled due to winter storm.
Mar.17.	Properties of determinants. Proof of the determinant criterion for invertibility. Notes. Homework 9 (due Sun. Mar. 28.): 3.1: 4, 10, 14, 20, 24; 3.2: 16, 18, 20, 22; 3.3: 20, 22.
Mar.19.	More applications of determinants. Determinants and area/volume. Notes.
Mar.22.	Abstract vector spaces: definitions, examples, and generalizations of familiar facts. Notes.
Mar.24.	Relating vector spaces to R^n via coordinate mappings. Row spaces and row ranks. Notes. Homework 10 (due Wed. Mar. 31.): 4.1: 6, 8, 12, 16, 18; 4.2: 10, 12; 4.4: 28; 4.6: 2, 4, 6, 8.
Mar.26.	Homework discussion. Notes. Midterm II date announced: April 5.
Mar.29.	Change of basis. Notes. Details and review problems on Midterm II.
Mar.30.	Algorithm for computing transition matrices. Matrices of linear maps. Notes. Homework 11 (due Wed. Apr. 7.): 4.6: 10, 12; 4.7: 2, 4, 8, 10; 5.4: 1, 2, 3, 4.
Apr.02.	Eigenvectors and eigenvalues: motivation, definition, and first examples. Notes. Solutions to Midterm II review problems.
Apr.05.	Discussion of the midterm review. Notes.
Apr.07.	Characteristic polynomials. Finding eigenvalues. Notes. Homework 12 (due Wed. Apr. 14.): 5.1: 3, 6, 8, 12, 14; 5.2: 4, 6, 10, 16.
Apr.09.	Eigenspaces and their bases. Algebraic vs. geometric multiplicity. Notes.
Apr.12.	Diagonalizability and diagonalization. Notes.
Apr.14.	More diagonalization problems. Why the formula A=PDP^{-1} works. Notes. Homework 13 (due Wed. Apr. 21.): 5.3: 2, 4, 8, 12, 14; 5.4: 12, 14, 16.
Apr.16.	Matrices of linear maps, revisited. Homework discussion. Notes.
Apr.19.	Complex eigenvalues. Inner products, length, and distance. Final Exam announced (available on Canvas from 11:59 am to 11:59 pm of May 5). Notes.
Apr.21.	Unit vectors and normalization. Orthogonality via inner products. Orthogonal sets. Notes. Homework 14 (due Wed. Apr. 28.): 6.1: 2, 5, 10, 14; 6.2: 8, 10, 12, 14; 6.3: 2, 6, 8, 10, 12.
Apr.23.	Orthogonal and orthonormal bases. Orthogonal projections. Notes. Details on final exam and review for Chapters 5 and 6..
Apr.26.	More on orthogonal projections. The Gram-Schmidt algorithm. Notes.
Apr.28.	Review for final exam.