Math 520: Linear Algebra (Spring 2018)

Section S03

Instructor: Shamil Asgarli Lecture Time: MWF 12:00 - 12:50 pm
Email: shamil_asgarli@brown.edu Lecture Location: Barus & Holley 161
My office: Kassar House, Room 020 Office hours: Wednesdays 3-5 pm

Click here for the syllabus.

Exam Information:
Midterm 1
Solutions
Midterm 2 Solutions
Final Exam: May 11, 9:00 am -12:00 pm in Salomon Center DECI
Click here to read about the (optional) Final Project.

Homework. Click here to see the homework.


Quizzes. 
  
Quiz 1
 Solution Quiz 6 Solution
Quiz 2  Solution Quiz 7 Solution
Quiz 3  Solution Quiz 8 Solution
Quiz 4  Solution Quiz 9 Solution
Quiz 5
 Solution Quiz 10 Solution


Notes on some topics.  Sometimes I will type notes to expand upon particular concepts from class. They can be found below:

Note 1. Dimension of a Subspace.
Note 2. Discovering the 3 x 3 Determinant.
Note 3. Determinant of the Transpose.


Class Notes. The notes below are kindly provided by Kanika Gupta, one of the students in the class. The notes will be posted once a week (usually on the weekend).

Notes Date Topic Notes Date Topic
Lecture 1 Jan 24 System of linear equations
Lecture 21 Mar 14
Properties of Determinants
Lecture 2 Jan 26 System of linear equations
Lecture 22
Mar 16
Cramer's Rule
Lecture 3 Jan 29 Row reduction / echelon form
Lecture 23
Mar 19
Introduction to Vector Spaces
Lecture 4 Jan 31 Vector equations
Lecture 24
Mar 21
Subspaces of Vector Spaces
Lecture 5 Feb 2 Matrix equations
Lecture 25
Mar 23
Kernel & Range; Linear Independence
Lecture 6 Feb 5 Solution sets of Linear Systems
Lecture 26
Apr 2
Linear Independence, and Spanning
Lecture 7 Feb 7 Applications to Chemistry & Econ.
Lecture 27
Apr 4
Isomorphism of vector spaces
Lecture 8 Feb 9 Linear independence
Lecture 28
Apr 6
Coordinates relative to a basis; Dimension
Lecture 9 Feb 12 Linear independence + Transformations
Lecture 29
Apr 9
Basis Theorem + Change of Basis
Lecture 10 Feb 14 Linear transformations (continued) Lecture 30 Apr 11
Review session for Midterm 2
Lecture 11 Feb 16 Matrix of a linear transformation
Lecture 31
Apr 13
Change of Basis (cont.) + Row Space
Lecture 12 Feb 21 Surjective and injective transformations
Lecture 32
Apr 16
Rank-Nullity for abstract vector spaces
Lecture 13 Feb 23 Matrix operations
Lecture 33
Apr 18
Eigenvectors and Eigenvalues
Lecture 14 Feb 26 Invertible Matrices
Lecture 34
Apr 20
Char. Polynomial; linear independence result
Lecture 15 Feb 28 Invertible Matrices (continued)
Lecture 35
Apr 23
Similarity; Diagonalization
Lecture 16 Mar 2 Invertible Matrix Theorem
Lecture 36
Apr 25
Diagonalization; Matrix of a transformation
Lecture 17 Mar 5 Subspaces of R^n
Lecture 37
Apr 27
Matrix of a linear transformation (cont.)
Lecture 18 Mar 7 Column space and null space
Lecture 38
Apr 30
Inner Products
Lecture 19 Mar 9 Dimension of a subspace, and rank
Lecture 39
May 2
Orthogonal Complements
Lecture 20 Mar 12 Introduction to Determinants
Lecture 40
May 4
Orthogonal Lists and Orthogonal Projection