### Handouts

### Exams

- Midterm 1: Friday, February 3, 2017 (in class). Solutions for midterm 1.
- Midterm 2: Friday, March 10, 2017 (in class). Solutions for midterm 2.
- Final exam (
__CUMULATIVE__): Tuesday May 2, 2017, 12:00pm-1:45pm (location: Scott Lab N048 (usual lecture room)).

### Quizzes

There will be 11 quizzes throught the semester. Each quiz will contain exercises from the corresponding homework problem suggestions. The lowest quiz score will be dropped.- Quiz 1: Wednesday, January 18, 2017 (in class). Topics: § 1.1 - 1.2. Solutions.
- Quiz 2: Friday, January 27, 2017 (in class). Topics: § 1.3, 1.5-1.6. Solutions.
- Quiz 3: Friday, February 10, 2017 (in class). Topics: § 2.1-2.3. Solutions.
- Quiz 4: Friday, February 17, 2017 (in class). Topics: § 2.4, 3.1-3.3. Solutions.
- Quiz 5: Wednesday, February 22, 2017 (in class). Topics: § 3.4-3.5. Solutions.
- Quiz 6: Wednesday, March 1, 2017 (in class). Topics: § 5.2-5.4 Solutions.
- Quiz 7: Friday, March 24, 2017 (in class). Topics: § 5.7. Solutions.
- Quiz 8: Friday, March 31, 2017 (in class). Topics: § 5.8-5.9, 6.2. Solutions.
- Quiz 9: Friday, April 7, 2017 (in class). Topics: § 6.3-6.4. Solutions.
- Quiz 10: Friday, April 14, 2017 (in class). Topics: § 4.1-4.2, 4.4. Solutions.
- Quiz 11: Friday, April 21, 2017 (in class). Topics: § 4.5-4.7. Solutions.

### Homework problems suggestions

The homework problems are designed to understand the material discussed during the lectures. Each quiz will consist of problems from the corresponding assignment. Extra homework assignments cover topics included in the midterms and finals but not on the quizzes.- Homework 1:
**§ 1.1:**1, 5, 6, 7, 11, 15, 16, 24, 31, 32;

**§ 1.2:**1, 8, 12, 13, 22, 31, 36, 41, 47, 50, 52. - Homework 2:
**§ 1.3:**1, 4, 6, 10, 14, 19, 21, 23, 26, 28 ;

**§ 1.5:**1, 8, 14, 22, 25, 29, 31, 34, 42, 48, 54, 68;

**§ 1.6:**4, 7, 11, 13, 14, 20, 41, 42.

Solutions to even problems. - Extra homework:
**§ 1.7:**1, 11, 19, 27, 29, 33, 41, 50, 51, 55 ;

**§1.9:**1, 7, 9, 17, 19, 21, 23, 27, 28, 35, 39, 41. - Homework 3:
**§ 2.1:**1, 5, 6, 10, 15, 19, 26, 28, 30, 35;

**§ 2.2:**1, 5, 8, 12, 22, 25, 28, 30, 33;

**§ 2.3:**1, 4, 8, 13, 16, 19, 23, 32, 34, 42, 48. - Homework 4:
**§ 2.4:**1, 3, 5, 7, 9, 11, 17, 21, 23, 25;

**§ 3.1:**1, 7, 9, 12, 13, 17, 21;

**§ 3.2:**1, 6, 7, 8, 9, 17, 18, 19, 29, 30, 31;

**§3.3:**1, 11, 15, 17, 21, 23, 27, 35, 37, 45.

Solutions to even problems. - Homework 5:
**§ 3.4:**1, 9, 11, 16, 17, 21, 25, 29, 33, 36;

**§ 3.5:**1, 3, 13, 15, 20, 22, 26, 29, 31, 35.

Solutions to even problems. - Homework 6:
**§ 5.2:**1, 2, 3, 6, 9, 10, 19, 25, 29, 31, 33, 36;

**§ 5.3:**1, 4, 5, 9, 11, 13, 19, 23, 25, 27, 28, 29, 31;

**§ 5.4:**1, 4, 5, 9, 10, 13, 15, 19, 23, 24, 26, 27, 28.

Solutions to even problems. - Extra homework:
**§ 3.6:**1, 5, 7, 9, 11, 13, 17, 19 ;

**§ 3.7:**1, 3, 4, 5, 8, 10, 15, 19, 20, 21, 23, 25, 29, 36.

Solutions to even problems. - Homework 7:
**§ 5.7:**1, 2, 3, 5, 7, 9, 11, 12, 13, 14, 15, 19, 20, 27.

Solutions to even problems. - Homework 8:
**§ 5.8:**1, 2, 3, 5, 9, 10, 11, 23, 25;

**§ 5.9:**1, 2, 3, 7, 9, 11, 13, 15, 17, 19, 23;

**§ 6.2:**1, 7, 11, 13, 17, 21, 29.

Solutions to even problems. - Homework 9:
**§ 6.3:**1, 5, 7, 19, 21, 23;

**§ 6.4:**1, 5, 7, 9, 13, 15, 17, 25. - Homework 10:
**§ 4.1:**1, 3, 11, 13, 15, 17, 19;

**§ 4.2:**27, 29;

**§ 4.4:**3, 7, 9, 11, 13, 23, 25. - Homework 11:
**§ 4.5:**1, 5, 9, 11, 12, 17, 18, 19;

**§ 4.6:**1, 3, 5, 7, 9, 13, 19, 21, 23, 25, 27, 29;

**§ 4.7:**1, 3, 7, 11, 13, 17, 19, 26, 27.

### Lectures

- Lecture 1 (§ 1.1: Introduction to Matrices And Systems of Linear Equations), January 9, 2017.
- Lecture 2 (§ 1.1 (cont.): Introduction to Matrices And Systems of Linear Equations, and § 1.2: Echelon Form and Gauss-Jordan Elimination), January 11, 2017.
- Lecture 3 (§ 1.2 (cont.): Echelon Form and Gauss-Jordan Elimination), January 13, 2017.
- Lecture 4 (§ 1.3: Consistent Systems of Linear Equations), January 18, 2017.
- Lecture 5 (§ 1.3 (cont.): Homogeneous System, and § 1.5: Matrix Operations), January 20, 2017.
- Lecture 6 (§ 1.5 (cont.): Matrix multiplication, and § 1.6: Algebraic Properties of Matrix Operations), January 23, 2017.
- Lecture 7 (§ 1.7: Linear Independence and Nonsingular Matrices), January 25, 2017.
- Lecture 8 (§ 1.7 (cont.): Nonsingular Matrices, and § 1.9: Matrix Inverses and Their Properties), January 27, 2017.
- Lecture 9 (§ 1.9 (cont.): Matrix Inverses and Their Properties), January 30, 2017.
- Lecture 10 ( § 2.1: Vectors in the Plane, and § 2.2: Vectors in Space), February 6, 2017.
- Lecture 11 (§ 2.3: The Dot Product and the Cross Product), February 8, 2017.
- Lecture 12 (§ 2.3 (cont.): The Cross Product, and § 2.4: Lines And Planes in Space), February 10, 2017.
- Lecture 13 ( § 2.4 (cont.): Planes in Space; § 3.1: Introduction to the Vector Space
**R**, and § 3.2: Vector Space Properties of^{n}**R**), February 13, 2017.^{n} - Lecture 14 (§ 3.3: Examples of Subspaces), February 15, 2017.
- Lecture 15 (§ 3.4: Bases for Subspaces), February 17, 2017.
- Lecture 16 (§ 3.4 (cont.): Bases for Subspaces, and § 3.5: Dimension), February 20, 2017.
- Lecture 17 (§ 5.1: Introduction to Vector Spaces and Linear Transformations, and § 5.2: Vector Spaces), February 22, 2017.
- Lecture 18 (§ 5.3: Subspaces), February 24, 2017.
- Lecture 19 (§ 5.4: Linear Independence, Bases and Coordinates), February 27, 2017.
- Lecture 20 (§ 3.6: Orthogonal Bases for Subspaces), March 1, 2017.
- Lecture 21 (§ 3.7: Linear Transformation from
**R**to^{n}**R**), March 3, 2017.^{m} - Lecture 22 (§ 3.7 (cont.): Linear Transformation from
**R**to^{n}**R**), March 6, 2017.^{m} - Lecture 23 (§ 5.7: Linear Transformations on abstract vector spaces), March 20, 2017.
- Lecture 24 (§ 5.7 (cont.): Linear Transformations, and § 5.8: Operations With Linear Transformations), March 22, 2017.
- Lecture 25 (§ 5.8 (cont.): Operations With Linear Transformations), March 24, 2017.
- Lecture 26 (§ 5.9: Matrix Representations Of Linear Transformations), March 27, 2017.
- Lecture 27 (§ 5.9 (cont.): Matrix Representations Of Linear Transformations, and § 6.1: Introduction to Determinants and § 6.2: Cofactor Expansions Of Determinants), March 29, 2017.
- Lecture 28 (§ 6.3: Elementary Operations And Determinants), March 31, 2017.
- Lecture 29 (§ 6.4: Cramer's Rule), April 3, 2017.
- Lecture 30 (§ 4.1: The Eigenvalue Problem for (2 × 2) Matrices, and § 4.2: Determinants and the Eigenvalue Problem), April 5, 2017.
- Lecture 31 (§ 4.4: Eigenvalues and the Characteristic Polynomial), April 7, 2017.
- Lecture 32 (§ 4.5: Eigenvectors and Eigenspaces), April 10, 2017.
- Lecture 33 (§ 4.5 (cont.): Eigenvectors and Eigenspaces), April 12, 2017.
- Lecture 34 (§ 4.6: Complex Eigenvalues and Eigenvectors), April 14, 2017.
- Lecture 35 (§ 4.6 (cont.): Complex Eigenvalues and Eigenvectors, and § 4.7: Similarity Transformations and Diagonalization), April 17, 2017.
- Lecture 36 (§ 4.7 (cont.): Similarity Transformations and Diagonalization), April 19, 2017.