# Daily Syllabus, Math 221 Linear Algebra, Fall 2023

Be sure to check back, because this will be updated during the semester.

• All section numbers refer to the 3rd and 4th editions of Linear Algebra and Its Applications by Lay.
• PCA due refers to Pre-Class Assignments submitted through Canvas
• PS due refers to Problem Sets uploaded to Canvas

Week Major Topics Tuesday
9:30 - 11:50
Thursday
9:30 - 11:50
1 Welcome to Linear Algebra!
Systems of linear equations and equivalent vector equations

Background Questionnaire due
Upload photo to profile in Canvas
8/29 1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
8/31 1.3 Vector Equations
2 Describing all solutions to a system

PCA due Monday 9/4 @ 11:59 pm
9/5 1.4 The Matrix Equation Ax=b
1.5 Solution Sets of Linear Systems
9/7 1.7 Linear Independence

PS #1 & partner eval due @ 11:59 pm
3 Matrices as functions

PCA due Monday 9/11 @ 11:59 pm
9/12 1.8 Introduction to Linear Transformations 9/14 1.9 The Matrix of a Linear Transformation

PS #2 & partner eval due @ 11:59 pm
4 Multiplying and inverting matrices

PCA due Monday 9/18 @ 11:59 pm
9/19 2.1 Matrix Operations
2.2 Inverse of a Matrix
9/21 2.3 Characterizations of Invertible Matrices

PS #3 & partner eval due @ 11:59 pm
5 Using matrices to shift, rotate, and skew graphics; The determinant function

Do the reading, but no PCA to submit
9/26 Cheat Sheet for Exam 1 due @ 8:00 am
Exam 1, In-Class part, 9:30 - 10:15

Exam 1 covers thru 2.3
9/28 2.7 Applications to Computer Graphics 3.1 Introduction to Determinants

Exam 1, Takehome part, due
Fri 9/29 @ 11:59 pm
6 Identifying underlying structural similarities

PCA due Monday 10/2 @ 11:59 pm
10/3 3.2 Properties of Determinants 4.1 Vector Spaces and Subspaces 10/5 4.2 Null Spaces, Column Spaces, and Linear Transformations
7 No class meetings this week due to Fall Break and MAP Day 10/10 Fall Break 10/12 MAP Day
8 Minimal generating sets

PCA due Monday 10/16 @ 11:59 pm
10/17 4.3 Linearly Independent Sets; Bases 10/19 4.3 Linearly Independent Sets; Bases (cont.)

PS #4 & partner eval due @ 11:59 pm

PCA due Monday 10/23 @ 11:59 pm
10/24 4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
10/26 4.6 Rank

PS #5 & partner eval due @ 11:59 pm
10 Understanding longterm behavior; Directions fixed by matrix functions

PCA due Monday 10/30 @ 11:59 pm
10/31 4.9 Applications to Markov Chains 11/2 5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation

PS #6 & partner eval due @ 11:59 pm
11 Extending geometric intuition to higher dimensions

PCA due Monday 11/6 @ 11:59 pm
11/7 6.1 Inner Product, Length, and Orthogonality

Cheat Sheet for Exam 2 due @ 8:00 am
Exam 2, In-Class part, 9:30 - 10:00
Exam 2 covers thru 5.2
11/9 6.2 Orthogonal Sets

Exam 2, Takehome part, due @ 11:59 pm
12 Finding the closest vector

PCA due Monday 11/13 @ 11:59 pm
11/14 6.3 Orthogonal Projections
6.4 The Gram-Schmidt Process
11/16 6.5 Least-Squares Problems
13 A factorization of certain square matrices

PCA due Monday 11/20 @ 11:59 pm
11/21 5.3 Diagonalization 11/23 Thanksgiving Break
14 A factorization of m x n matrices

PCA due Monday 11/27 @ 11:59 pm
11/28 7.1 Diagonalization of Symmetric Matrices 11/30 7.4 The Singular Value Decomposition

PS #7 (individual) due @ 11:59 pm
15 The power of the singular value decomposition

PCA due Monday 12/4 @ 11:59 pm
12/5 Applications of the SVD

Cheat Sheet for Exam 3 due Wednesday 12/6 @ 8:00 am
12/7 The BIG Picture
Finals Period 12/12 Exam 3 due Wednesday 12/13 @ 11:59 pm 12/14