## Math 2101-002 Linear Algebra. Fall 2019

### Important Information

First day of classes: Tuesday January 15.
Last day to drop (tuition refund available): Monday, January 28.
Last day to withdraw (no refund): Monday, March 18.
Spring Break: March 4-8
Last Class: Thursday, April 25.
Final Exam: Tuesday, May 7, 10:30-12:30.

Please note: If a student misses the final exam for some reason such as an illness, and the student fails to contact the professor before the grades are turned in, the course grade will be an F.

### Syllabus, including textbook information and office hours.

#### Proposed timetable (sections to be covered). Actual timetable:

Tuesday 15 January: Sections 1.1, 1.2 (linear equations, Gaussian elimination)
Thursday 17 January: Sections 1.2, 2.1, 2.3 (Gaussian elimination, Upper Echelon form, Consistent systems)
Tuesday 22 January: Sections 2.3, 2.4, 2.5 (Consistent systems, Homogeneous aand non-homogeneous systems)
Thursday 24 January: Review of Chapter 2. (including equivalent conditions for unique solution of Ax=b)
Tuesday 29 January: Sections 3.2, 3.5, and 3.6 (Vector, Matrices, operations)
Thursday 31 January: Sections 3.3, 3.4 (linear maps, composition of linear maps)
Tuesday 5 February: Section 3.7 (Inverse of a matrix)
Thursday 7 February: More on section 3.7 (Inverse of a matrix) (We also had a quiz, and here are the responses.)
Tuesday 12 February: Sections 3.8, 3.9, 3.10 (Inverse of a rank-one update, elementary matrices, application to finding upper Echelon form)
Thursday 14 February: Section 3.10 (LU factorization)
Tuesday 19 February: Sections 4.1, 4.2 (Vector spaces, subspaces) (We also had a quiz, and here are the responses.)
Thursday 21 February: Section 4.3 (The four fundamental subspaces, linearly in/dependent vectors).
Tuesday 26 February: Exam 1, and here are the responses.
Thursday 28 February: Review Sections 4.1-4.3.
Tuesday 12 March: Section 4.4 (basis, dimension of subspaces)
Thursday 14 March: Sections 4.5, 4.7 (more on rank, linear transformations, matrix of a linear transformation)
Tuesday 19 March: Review of section 4.7. Section 5.1 (norms). Quiz on Chapter 4, and here are the responses.
Thursday 21 March: More on Section 5.1, Sections 5.3, 5.4 (Inner products, norms, angle between vectors, orthogonal vectors)
Tuesday 26 March: Section 5.2 (Matrix norms, orthogonal matrices), Section 5.5 (Gram-Schmidt orthogonalization process, QR Factorization). Section 5.6 (Orthogonal matrices). Example of Gram-Schmidt and QR.
Thursday 28 March: Review of Section 5.5 (Gram-Schmidt and QR), more on Section 5.6 (Orthogonal matrices).
Tuesday 2 April: Sections 5.9, 5.11 (Complementary subspaces, oblique projections, orthogonal projections).
Thursday 4 April: Section 5.12 (Singular Value Decomposition)
Tuesday 9 April: More on projections, and on the SVD.
Thursday 11 April. Exam 2 on chapters 4 and 5. Answers to this exam
Tuesday 16 April. Sections 6.1 and 6.2 (Determinants)
Thursday 18 April. Section 7.1 (Eigenvalues and Eigenvectors)
Tuesday 23 April. Sections 7.1 and 7.2 (and a little on 7.3) (more on Eigenvalues and Eigenvectors, diagonalizable matrices, equivalent matrices)

Special review session. Wednesday 1 May, 2 pm, Room 527 Wachman Hall.

#### Homework

Homework set number 1, due Tuesday 22 January. Answers to this set
Homework set number 2, due Thursday 24 January. Answers to this set
Homework set number 3, due Tuesday 29 January. Answers to this set
Homework set number 4, due Tuesday 5 February. Answers to this set
Homework set number 5, due Thursday 7 February. Answers to this set
Homework set number 6, due Tuesday 12 February. Answers to this set
Homework set number 7, due Thursday 14 February. Answers to this set
Homework set number 8, due Tuesday 19 February. Answers to this set
Homework set number 9, due Thursday 21 February. Answers to this set
Homework set number 10, due Thursday 28 February. Answers to this set
Homework set number 11, due Thursday 28 March. Answers to this set
Homework set number 12, due Tuesday 2 April. Answers to this set
Homework set number 13, due Thursday 4 April. Answers to this set
Homework set number 14, due Tuesday 9 April. Answers to this set
Homework set number 15, due Tuesday 23 April. Answers to this set

Office Hours:
Tuesdays 14:30 (Room 519)
Wednesdays 14:00 (Room 506)
Thursdays 14:30 (Room 519)