Welcome to the course! Meetings and communication: AC meetings AC Class meetings Tuesday, 3:45-5:00 pm PT AC Office hours Monday, 3:30-4:30 pm PT Email kanarsky@stanford.edu Any time

Introduction (mine): MS Applied Math (Moscow State University, Russia) 1993 PhD Mathematics, MS Computer Science (Emory University, Atlanta) 2000 Taught Mathematics and Statistics in community colleges (Ohlone, DVC) Tutored various EPGY courses since 2011 Last three years: teaching university-level math courses at SPCS

Introduction (yours): Name Your grade level at school (in the pod) Where do you live? (on the map) Answer a question: if you happen to have few hours of free time, what would you do? (in the pod)

Pass/Fail could use parent proctoring Assessments: Two exams (midterm and final). No other assignments are to be submitted. Proctoring: Pass/Fail could use parent proctoring Letter Grade independent proctoring ( a teacher/counselor at school etc.) you receive a letter grade only when both exams are independently proctored you may switch a “letter grade” to a “non-letter grade” Proctor registration: you will register your proctor through the website (information will be provided) proctor will download/upload the exam through the proctor’s page Grading: The grading scale is: A: 86-100 A-: 83-85 B+: 80-82 B: 76-79 B-: 73-75 C+: 70-72 C: 65-69 C-: 60-64 NP: <60 The Pass/Fail scale: CR: 60-100 NP: <60 The course grade is the average of scores obtained on two exams.

What should you be ready for? To do a lot of independent work from the start! To allocate several hours per week for studying What should you expect? My prompt response to your messages on any issues (administrative or subject-related). My extensive feedback to your exam solutions. What should I expect from you? Your desire to learn and advance! Communicating with me for help when needed! I ask to be specific in your email: - indicate your course and your full name (and preferred name if there is one) - if asking about a problem from the textbook or a lecture, include the image of the problem or retype it

Weekly work: Listen to the lectures lagunita.stanford.edu Do online exercises course lectures/”Downloads” Read corresponding sections of the textbook Linear Algebra, by Bronson Do offline exercises download from “Downloads”

A matrix: Definition, notation a p × n matrix Give notation, define the size, and address elements. Which are square? Example:

Example:

Matrix operations : Addition properties of matrix addition Exercises:

Matrix operations: Scalar multiplication properties of scalar multiplication

Matrix operations : Multiplication Example: Each entry of AB is the product of a row and a column:

Understanding notation:

Practicing notation: For matrices A∈ 100 x 90 and B ∈ 90 x 80 set up the formula for the element of C=AB in the position (20,30).

Exercises: properties of matrix multiplication

Example: Exchanging rows

Multiplying a matrix by a column: two ways multiplying a row at a time multiplying a column at a time a combination of the three columns of A

Multiplying matrices: yet two more ways Row and Column Partitioning in row vectors in column vectors

Multiplying matrices: using row partitioning first row of C=AB row i of AB is the product of a row i of A times B (“a row by a matrix”)

Multiplying matrices: using column partitioning first column of C=AB column j of AB is the product of A and the column j of B (“a matrix by a column”)

Example: partitioning Questions:

COLLABORATE: Discuss: Is the statement below correct? Try a 2x2 example.

Matrix operations : Transposition properties of matrix transposition

Example: Matrix equations

Powers of Matrices: Must A be a square matrix? k times

Special Matrices: symmetric matrix skew-symmetric matrix diagonal matrix