MATH 3A

Welcome to Math 3A – linear fun! In this course, we will learn how to solve systems of equations and interpret them geometrically, and there will be lots of miracles. This is math at its finest! On this page you can find the syllabus, suggested homework, and practice exams. Enjoy the ride!


Syllabus

Math 3A – Syllabus


Lecture Notes and Videos

# Lecture Notes YouTube Videos
1 Systems of Equations Row-reduction
Inconsistent Systems
2 Row-Reduction and Echelon Forms Infinitely many solutions
Solving ax + by
3 Vectors and Ax = b
4 Span and Ax = 0 Span
Row Theorem
5 Linear Independence Linear Independence
6 Linear Transformations (I) Showing T is linear
7 Linear Transformations (II) Matrix of T and One-to-one and Onto
Rotation Matrix
8 Matrix Algebra Matrix Multiplication
AB vs BA
9 The Inverse of a Matrix Finding A-1
Product of elementary matrices (optional)
LU Factorization (optional)
10 Invertible Matrix Theorem + Subspaces Show A is invertible
Invertible matrices must be square
Show H is a subspace
Show H is not a subspace
Span is a subspace
11 Nul(A) and Col(A) Nul(A)
Nul(A) is a subspace
Checking something is a basis
12 Dimension and Rank Basis and dimension
Nul(A), Col(A), Rank(A)
Coordinates
Infinite-dimensional space (optional)
Rank 1 Matrices and Outer Products (optional)
13 Determinants Determinants
Determinants and row-reduction
More determinants and row-reduction
Determinants and Invertibility
14 Applications of Determinants Cramer’s Rule
A-1 using determinants
Area of parallelogram
Determinants and volumes
15 Midterm – Review 111 True/False Questions
16 Midterm
17 Eigenvalues and Eigenvectors Diagonalize 2×2 matrix
18 Diagonalization Diagonalize 3×3 matrix
Diagonalization analogy
Complex Eigenvalues (optional)
19 Diagonalizability Not diagonalizable
20 B-Matrices B-matrix of A
Derivative in a box (optional)
Matrix of a matrix (optional)
21 Applications of Diagonalization Pokemon Battle
Fibonacci Sequence
Matrix Limit 1
Matrix Limit 2
Square root of a matrix
Matrix exponential
Cos of a matrix
Systems of differential equations (optional)
22 Dot products and lengths
23 Orthogonality Awesomeness Orthogonal Sets
24 Orthogonal Projections Orthogonal Projections
Proof of Cauchy-Schwarz
Awesome Cauchy-Schwarz (optional)
25 The Gram-Schmidt Process Gram-Schmidt Process
QR Decomposition
26 Least-Squares Least Squares
Linear Models
27 Final Review 1 Symmetric Matrices (optional)
Quadratic Forms (optional)
28 Final Review 2
29 Final Review 3 Linear Algebra Overview
111 True/False Questions

 


Suggested Homework

Suggested Homework is not to be turned in, but important for the quizzes and the exams. Remember that the lowest 2 quizzes are dropped and that there are no quizzes on Th 09/26 (Week 0) and on Th 11/28 (Thanksgiving)

Hints/Solutions to some of the problems: Solution – Bank (from an older edition, so be careful)

Homework “Due Date” Problems
Homework 1 October 3 1.1: 11, 13, 21, 23, 24, 28
1.2: 11, 19, 21, 22, 24, 25, 30
1.3: 11, 17, 23, 24, 25, 26
1.4: 23, 24, 25, 31
Homework 2 October 10 1.4: 22
1.5: 9, 11, 23, 24, 31, 32
1.7: 2, 7, 11, 17, 21, 22, 27, 34, 37
1.8: 15, 17, 21, 32, 33, 35
1.9: 3, 8, 10
Homework 3 October 17 1.8: 3, 11, 22, 34
1.9: 23, 24, 25, 27
2.1: 2, 3, 9, 10, 15, 16, 24, 25, 27
2.2: 1, 5, 9, 10, 18, 21, 29, 31
Homework 4 October 24 2.3: 5, 11, 12, 16, 18, 30, 33
2.8: 1, 2, 7, 9, 13, 17, 21, 22, 25, 31
2.9: 1, 3, 10, 16, 17, 18, 20, 25
Homework 5 October 31 3.1: 3, 13, 37, 39, 40
3.2: 5, 23, 27, 28, 32, 33, 34, 35, 39
3.3: 3, 13, 18, 22, 31, 32
Homework 6 November 7 5.1: 5, 10, 15, 21, 22, 24, 25, 26, 32
5.2: 1, 7, 9, 15, 19, 21, 22, 24
Homework 7 November 14 5.3: 1, 9, 13, 21, 22, 23, 24, 27, 31, 32
5.4: 11, 13, 17, 19, 20, 21, 22, 23
Homework 8 November 21 5.3: Applications
6.1: 1, 5, 10, 14, 17, 19abc, 20abd, 22, 24, 28
6.2: 1, 7, 17, 20, 23abc, 24ab
Homework 9 December 5 6.1: 19de, 20ce, 31
6.2: 11, 13, 15, 23de, 24cde, 25
6.3: 3, 10, 11, 17, 21, 22
6.4: 3, 7, 9, 17, 18
6.5: 3, 7, 9, 13, 15, 17, 18, 24, 25
6.6: 4

 



Useful links

My Youtube Channel

Playlist Link
Chapter 1 Linear Equations in Linear Algebra
Chapter 2 Matrix Algebra
Chapter 3 Determinants
Chapter 5 Eigenvalues and Eigenvectors
Chapter 6 Orthogonality
Fun topics Linear Algebra

 


Exams

Here you can find information about the exams, as well as other goodies such as practice exams.

Midterm Exam: Friday, November 1, 2 – 2:50 PM in 178 HH

Covers Chapters 1, 2, and 3

Study Guide Study Guide
Chapter 1 – Playlist Linear Equations
Chapter 2 – Playlist Matrix Algebra
Chapter 3 – Playlist Determinants
Practice Exam Solutions Comments
Peyam 1 Solutions Midterm (Fall 2019)
Peyam 2 Solutions Midterm (Winter 2019)
Peyam 3 Solutions
Peyam 4 Solutions
Peyam 5 Solutions
Vojta 1 Solutions Ignore 1ef and 5
Vojta 2 Solutions
Ribet Solutions Ignore 1, 2abe, 3b
Sample T/F Solutions Ignore 1g, 2cef, 3i, 4fgh
Old Review Solutions Ignore 5, 10, 11
Old Quiz 1 Solutions
Old Quiz 2 Solutions
Old Quiz 3 Solutions
Old Quiz 4 Solutions Ignore 1
Old Quiz 5 Solutions Only do 1bcd
111 True-False

Solutions

Video

Only do up to 70, and ignore 19, 41, 42, 52, 54, 59, 66, 68

Final Exam: Friday, December 13, 1:30 – 3:30 pm in 178 HH

Covers Chapters 1, 2, 3, 5, and 6

Warning: The Final Exam is cumulative, so make sure to also look at all the practice midterms for a complete review. Also, ignore any questions about row-spaces

Study Guide Study Guide
Chapter 1 – Playlist Linear Equations
Chapter 2 – Playlist Matrix Algebra
Chapter 3 – Playlist Determinants
Chapter 5 – Playlist Eigenvalues and Eigenvectors
Chapter 6 – Playlist Orthogonality
111 True-False Questions 111 True-False Questions

 

Practice Exam Solutions Comments
Peyam 1 Solutions Final Exam (Fall 2019)
Peyam 2 Solutions Final Exam (Winter 2019)
Peyam 3 Solutions Final Exam (Winter 2019)
Peyam 4 Solutions Only do 1-3
Peyam 5 Solutions Only do 1-3
Peyam 6 Solutions Only do 1abcd, 2, 3, 6
Peyam 7 Solutions Only do 1abde, 2, 4, 8, 9
Peyam 8 Solutions Ignore 1bf, 6, 7, 8, 10
Canez Solutions Only do 1, 4, 6-10
Vojta Solutions Ignore 1a, 7
Tataru Solutions Ignore 4, 5bd
Ribet Solutions Ignore 1a
Bergman Solutions Ignore 2ce, 5
Sample T/F Solutions Ignore 3a, 4bcdi
111 True-False

Solutions

YouTube Video

Ignore 19, 41, 42, 52, 54, 59, 66, 68, 85, 86, 104, 108 – 111
Old Review Solutions Only do 1, 3, 5
Old Quiz 6 Solutions Only do 1
Old Quiz 7 Solutions