2. 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
Any time

3. 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

4. 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)

5. 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.

6. 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
- 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

7. 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”

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

10. Example:

11. Matrix operations : Addition
properties of matrix addition
Exercises:

12. Matrix operations: Scalar multiplication
properties of scalar multiplication

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

14. Understanding
notation:

15. 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).

16. Exercises:
properties of matrix
multiplication

17. Example: Exchanging rows

18. 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

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

20. 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”)

21. 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”)

22. Example: partitioning
Questions:

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

26. Matrix operations : Transposition
properties of matrix
transposition

27. Example: Matrix equations

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

29. Special Matrices:
symmetric matrix
skew-symmetric matrix
diagonal matrix