Linear Algebra

**Extra Help: **
Math 1021
is a one-credit course that offers academic support for Math 2210.

The Math
Support Center offers free one-on-one tutoring.

**Academic Integrity:**
**
Course materials are intellectual property belonging to the lecturer. Students are not permitted to post (on the web), distribute, or sell any course materials (lectures, homework, exams). Such unauthorized behavior constitutes academic misconduct.**

Each student in this course is expected to
abide by the Cornell
University Code of
Academic Integrity.

In this
course, students may work alone or in
groups on the homework, but
should turn in all
homework individually.

**Exams:** Calculators, computers, notes, cheat sheets, and books are not allowed at the exams. Cell phones may not be used in the exam rooms, not even as time-keeping devices.

There are two prelims and
a final
exam.

The best way to prepare for the exam is to solve all homework problems.

Additional Practice Problems:

1.2: 11,25

1.3: 11,21

1.4: 11,23,31

1.5: 11,29

4.1: 3,13,21,29,34.

Topics:

Systems of linear equations (section 1.1)

Row reduction and echelon forms (section 1.2)

Vector spaces (sections 1.3 and 4.1)

Subspaces (section 4.1)

Linear combinations, Span (sections 1.3 and 4.1)

The matrix equation Ax = b (section 1.4)

Solution sets of linear systems (section 1.5).

Prelim 1 with solutions

The best way to prepare for the exam is to solve all homework problems.

Additional Practice Problems:

4.2: 15,24,29

1.7: 12,21

4.3: 15,25

4.4: 13

4.5: 14,24,26

6.1: 18,24

6.2: 23abc

6.3: 5

6.4: 4,9.

Topics:

Null spaces, column spaces (section 4.2)

Linear independence (sections 1.7 and 4.3)

Basis (section 4.3)

Coordinate systems (section 4.4)

The dimension of a vector space (section 4.5)

Inner product, length, and orthogonality (section 6.1)

Orthogonal sets (section 6.2)

Orthogonal projections (section 6.3)

The Gram-Schmidt process (section 6.4)

The best way to prepare for the exam is to solve all homework problems.

2017 Final Exam with solutions

Students with special needs should contact irena@math.cornell.edu at least 15 days before each exam.

If you miss both prelims, you should retake the course. If you miss one prelim, then your score on that prelim will be half of your score on the final exam. If you miss the final exam, you may receive grade Incomplete (if you are eligible) and take the exam next time when it is offered (most likely, in December 2018).

The best way to prepare for exams is to solve all homework problems.

**Grading:**

- Homework: 50 points
- Prelim 1: 100 points
- Prelim 2: 100 points
- Final exam: 200 points.

Grade B- or better is required in order to count the course as a prerequisite for the Math Major.

**Office hours: **

Irena Peeva, irena@math.cornell.edu, Wednesday and Friday 11:30-12:00 in MLT 547.

Viktor Kiss, vkiss@math.cornell.edu, Wednesday 2:00-2:30 and Friday 11:00-11:30 in MLT430.

Anwesh Ray, ar2222@cornell.edu, Tuesday 1:30-2:30 and Friday 4:30-5:00 in MLT.

Yun Liu, yl2649@cornell.edu, Wednesday 1:30-2:30 and Thursday 10:30-11:00 in MLT.

**Tentative list of topics:**

- Systems of linear equations (section 1.1)
- Row reduction and echelon forms (section 1.2)
- Vector spaces (sections 1.3 and 4.1)
- Subspaces (section 4.1)
- Linear combinations, Span (sections 1.3 and 4.1)
- The matrix equation Ax = b (section 1.4)
- Solution sets of linear systems (section 1.5)
- Null spaces, column spaces (section 4.2)
- Linear independence (sections 1.7 and 4.3)
- Basis (section 4.3)
- Coordinate systems (section 4.4)
- The dimension of a vector space (section 4.5)
- Inner product, length, and orthogonality (section 6.1)
- Orthogonal sets (section 6.2)
- Orthogonal projections (section 6.3)
- The Gram-Schmidt process (section 6.4)
- Introduction to linear transformations (sections 1.8. and 4.2)
- The matrix of a linear transformation (section 1.9)
- Matrix operations (section 2.1)
- The inverse of a matrix (section 2.2)
- Characterizations of invertible matrices (section 2.3)
- Rank (section 4.6)
- Introduction to determinants (section 3.1)
- Properties of determinants (section 3.2)
- Cramer's rule, Determinants as area or volume (section 3.3)
- Eigenvectors and eigenvalues (section 5.1)
- The characteristic equation (section 5.2)
- Diagonalization (section 5.3)
- Eigenvectors and linear transformations (section 5.4).

**Homework:** Homework will be collected in your TA section. Late homework will not be accepted (with the exception that students, who enroll late,
will be allowed to turn Homework1 in late). At the end of the semester, your lowest two homework scores will be dropped. Homework will be graded for effort; each homework set is 5 points. For feedback, one or two
homework problems will
be graded for correctness each week.
Answers to computational problems will be provided in your TA section.
Students may work together on homework, but must write up their
work individually.

Homework assignments will be posted here on Monday evening a week before the due date:

- Homework 1 due on Monday, Feb. 5

1.2: 4,12,14,16b,18,22,24,26,28,29,31. - Homework 2 due on Monday, Feb. 12

1.3: 2,4.

4.1: 2,6,8,23a,24b,28,30,32,33.

Let V be a real vector space. Let u, v, w be vectors in V.

Prove that the zero vector in V is unique, (see 4.1: 25).

Prove that the inverse (negative) vector of u in unique, (see 4.1: 26).

Prove that 0.u is equal to the zero vector, (see 4.1: 27).

If u+v=w+v, prove that u=w. - Homework 3 due on Monday, Feb. 26

4.1: 11,12,31,36.

1.3: 12,18,20,24d,24e,26.

1.4: 4,12,16,18,20,22. - Homework 4 due on Monday, March 5

1.4: 24,32,34,36.

1.5: 6,12,24a,26,38.

4.2: 2,6,16,26b,28,38,40.

- Homework 5 due on Monday, March 12

1.7: 10,14,22,28,30,36,38,40.

- Homework 6 due on Monday, March 19

4.3: 4,8,16,18,21abde,22,24,34.

4.4: 8,10,14. - Homework 7 due on Monday, March 26

4.5: 6,8,10,18,19,20,28,29,30. - Homework 8 due on Monday, April 9

6.1: 10,14,19,20,26,28.

6.2: 6,28.

6.3: 2,6.

6.4: 10,12. - Homework 9 due on Monday, April 16

- Homework 10 due on Monday, April 23

- Homework 11 due on Monday, April 30

- Homework 12 due on Monday, May 7