**Instructor:** Fedor Manin

**Sections** 0020 and 0075, Spring 2018

**Lecture**: 9:10AM MWF (section 0020), 12:40PM MWF (section 0075)

**Office**: Math Building 318 (not Math Tower 318 or Cockins Hall 318)

**Office hours**: 10:15–11:30AM Monday and Friday and 1:45–3:00PM Wednesday, or by appointment, or at additional times to be announced on Carmen.

**Textbook**: *Introduction to Linear Algebra* by Johnson, Riess, and Arnold

**Grader**: Yilong Wang

Click here for the syllabus and
**tentative** semester schedule. See also
Carmen.

**Homework 1**should be done by Wednesday, January 17 to prepare for the quiz on that day. Here are the textbook pages you need.**Homework 2**should be done by Friday, January 26 to prepare for the quiz on that day. Here are the textbook pages you need.**Homework 3**should be done by Friday, February 2 to prepare for the quiz on that day.**Homework 4**should be done by Friday, February 9 to prepare for Midterm I. I’ve also made a**list of topics**for Midterm I. Let me know if you think something is missing from it. I'll either add it in or tell you not to worry about it.**Homework 5**should be done by Friday, February 16 to prepare for the quiz on that day.**Homework 6**should be done by Friday, February 23 to prepare for the quiz on that day.

**Jan. 8th**: Introduction. What is a function? Linear equations.**Jan. 10th**: §1.1: Systems of linear equations. Geometry of solution sets in 2 and 3 dimensions. Every system of linear equations has zero, one, or infinitely many solutions. Elementary operations.**Jan. 12th**: §1.2: Gauss–Jordan elimination. Interpreting a matrix in reduced echelon form as a solution set to a system of equations.**Jan. 17th**: §1.3: More properties of solution sets.**QUIZ 1.****Jan. 19th**: §1.3, cont.: Properties of solution sets. Homogeneous systems of equations. §1.5: vectors and vector operations.**Jan. 22nd**: §1.5, cont.: Matrix operations. Matrix multiplication is function composition.**Jan. 24th**: §1.6: Properties of matrix operations. Transposes, miscellaneous notation.**Jan. 26th**:**QUIZ 2.**§1.7: Linear combinations.**Jan. 29th**: §1.7, cont.: Linear independence and nonsingular matrices.**Jan. 31st**: §1.9: Matrix inverses: intuition and proofs.**Feb. 2nd**:**QUIZ 3**. §1.9, cont.: Proof that nonsingular matrices have inverses, and review of nonsingular matrices.**Feb. 5th**: §1.9, cont.: Computing matrix inverses; properties of inverses.**Feb. 7th**: §1.6: Dot product and norm. Chapter 2: Lines and planes in ℝ^{2}and ℝ^{3}.**Feb. 9th**:**MIDTERM I.****Feb. 12th**: §3.1–3.2: Subspaces of ℝ^{n}: examples and non-examples.**Feb. 14th**: §3.3: Subspaces of ℝ^{n}: span of a set of vectors, range of a matrix.**Feb. 16th**:**QUIZ 4**. §3.3: Subspaces of ℝ^{n}: row space and null space (a.k.a. kernel) of a matrix.**Upcoming**: More about the null space. §3.4: Bases for subspaces.