Instructor: Mārtiņš Kālis

E-mail: martins@kalis.lv

Lectures: Wednesdays, 12.30–14.10, room 426 (auditorium 20)

Office hour: Tuesdays, 9.00-10.00, room 434

**Lecture **8 (25 March 2020) & **Lecture **9 (1 April 2020). Determinants.

– Practice problems: problems 4, 5, 8, 9, 11, 14 from section 4.1. (the other problems from the section are helpful, but optional).

Additional resources:

– Cramer’s Rule, Inverse Matrix, and Volume, MIT 18.06, Lectures 18, 19, 20

– “Linear algebra and its applications”, Gilbert Strang, chapter 4 (Determinants). available in the library.

**Midterm-homework.** The midterm graded homework replaces Quiz #2 and midterm exam scores for the final grade. The deadline for submissions ir 5 April 2020, 23:59.**Edit 2020-03-25**: 2(c) should read Solve A⃗x = b for (i) a = 1, ~~b~~**c** = 1, (ii) a = 1, ~~b~~**c** = 0, (iii) a = 0, ~~b~~**c** = 1.

**Lecture **7 (18 March 2020). **Independent study.** Please read sections 2.5 and 2.6, and do the practice problems below.

– Practice problems: problems 1, 3, 4, 9, 11, 13, 22 from section 2.7. (the other problems from the section are helpful, but optional).

Additional resources:

– 3blue1brown series “Essence of linear algebra“, episodes 6 & 7 (shared with lecture 6), episode 12.

– Projection Matrices and Least Squares, MIT 18.06, Lecture 16

– Cramer’s Rule, Inverse Matrix, and Volume, MIT 18.06, Lecture 20

– “Linear algebra and its applications”, Gilbert Strang, section 3.3. (Projections and least squares), available in the library.

**Lecture **6 (11 March 2020). Matrix recurrence relations (2.3), Non–singular matrices (2.5).

– Practice problems: problems 2–5 from section 2.4. (the other problems from the section are helpful, but optional).

Additional resources:

– 3blue1brown series “Essence of linear algebra“, episodes 6 & 7 (shared with lecture 7).

– Multiplication and Inverse Matrices, MIT 18.06, Lecture 3

– “Linear algebra and its applications”, Gilbert Strang, sections 1.6. (inverses and transposes), 2.2. (Solving Ax=0 and Ax=b), available in the library.

**Lecture **5 (4 March 2020). Matrices. Linear transformations.

– Practice problems: problem 1 from section 2.4

Additional resources:

– 3blue1brown series “Essence of linear algebra“, episodes 1–5.

– “Linear algebra and its applications”, Gilbert Strang, section 1.4., available in the library.

**Lecture **4 (26 Feb 2020). Field axioms. Matrices.

– Practice problems: 12, 13 (Chapater 1), example 2.1.2., problem 1 from section 2.4.

**Lecture 3** (19 Feb 2020). Homogeneus systems of equations. Arithmetic modulo p. Field axioms.

– Jupyter notebook from the lecture.

– Practice problems: 6, 7, 8, 9, 11 (Chapater 1)

– Optional: 14, 15, 16

Additional resources:

– Modular arithmetic on Khan Academy

– There will be a 30 minute quiz on Chapter 1 (except Field axioms) during the next lecture.

**Lecture 2** (12 Feb 2020). Gauss-Jordan method.

– Jupyter notebook from the lecture.

– Practice problems: 3, 4, 5 (Chapater 1)

Additional resources:

– Elimination with matrices, MIT 18.06, Lecture 2

– “Linear algebra and its applications”, Gilbert Strang, section 1.3., available in the library.

**Lecture 1** (5 Feb 2020). Introduction, (reduced-)row-echelon form, elementary row operations. Chapter 1 in course materials.

– Practice problems: 1, 2 (Chpater 1)

Additional resources:

– Column / row picture (will not be covered in depth), MIT 18.06, Lecture 1

– Elimination with matrices, MIT 18.06, Lecture 2

– “Linear algebra and its applications”, Gilbert Strang, section 1.3., available in the library.

**Exams**: There will be 4 quizes (M1a, ~~M1b,~~ M2a, M2b – out of 5), ~~1 midterm exam (P1 – out of 10)~~, 1 midterm graded homework (MT – out of 32) and 1 final exam (P2 – out of 10). You can retake the quizes and exams once. **Attendance bonus**: For each fully attended class, 1/4 bonus point will be received. (Maximum: 16/4 = 4 points)**Your grade** (out of 100) = bonus + 1.25(M1a+~~M1b~~+M2a+M2b) + ~~2.5~~*P1** MT + 5*P2

To pass the course, you must get at least ~~4 points~~ 40% in each — the midterm and the final exam.

## Course materials by Abuzer Yakaryilmaz

**Course materials:** download **Exam questions in 2019:** download **Exam questions in 2016:** download