Tuesdays and Thursdays, 9:10am-10:25am, 312 Mathematics

Dave Bayer (x42643, 426 Mathematics)

http://www.math.columbia.edu/~bayer/F99/linalg.html

**Exam 1**, Thursday, October 7, in class.

**Exam 2**, Thursday, November 11, in class.

**Final**, Thursday, December 16, 9:00am-NOON. Master University Examination Schedule

- Tuesday, 10:30am-11:30am
- Thursday, 2:00pm-3:00pm

- Chad Shampine, Tuesday, December 14, 1-3pm, 417 Math

- Dave Bayer, Wednesday, December 15, 7-9pm, 507 Math

- linalg_F99.pdf (all course materials in a single file)

- Practice Exam 1

- Exam 1

- Practice Exam 2

- Exam 2

- Practice Problems for Final

- Final Exam

- Final Exam Solutions (748 Kb)

- Tues, Sep 7:

1.1 Systems of Linear Equations. Exercises 1-8.

- Thurs, Sep 9:

1.2 Row Echelon Form. Exercises 1-3, 5, 6, 19.

- Tues, Sep 14:

1.3 Matrix Algebra. Exercises 1-10, 12, 20, 30.

- Thurs, Sep 16:

1.4 Elementary Matrices. Exercises 1-5, 7, 9, 15

- Tues, Sep 21:

1.5 Partitioned Matrices. Exercises 4, 5, 7-10.

- Thurs, Sep 23:

2.1 The Determinant of a Matrix. Exercises 1-4, 6, 10

- Tues, Sep 28:

2.2 Properties of Determinants.

- Thurs, Sep 30:

2.3 Cramer's Rule.

- Tues, Oct 5:

exam review

- Thurs, Oct 7:

**EXAM 1 (chapters 1 and 2)**

- Tues, Oct 12:

3.1 Vector Spaces. Exercises 1-10.

- Thurs, Oct 14:

3.2 Subspaces. Exercises 1-8.

- Tues, Oct 19:

3.3 Linear Independence. Exercises 1-9.

- Thurs, Oct 21:

3.4 Basis and Dimension. Exercises 1-8, 11

3.5 Change of Basis. Exercises 1-5, 8-10

- Tues, Oct 26:

3.6 Rowspace, column space. Exercises 1-7

- Thurs, Oct 28:

4.1 Linear transformations, definitions and examples.

4.2 Matrix representation of linear transformations.

- Tues, Nov 2:

**Election holiday; no class**

- Thurs, Nov 4:

4.3 Similarity.

- Tues, Nov 9:

exam review.

- Thurs, Nov 11:

**EXAM 2 (chapters 3 and 4)**

- Tues, Nov 16:

5.1 The scalar product. Exercises 1-8

5.2 Orthogonal subspaces. Exercises 1, 2

- Thurs, Nov 18:

5.3 Inner product spaces. Exercises 1-4

5.4 Least squares problems. Exercises 1-6

- Tues, Nov 23:

5.5 Orthonormal sets. Exercises 1, 2, 4, 7, 8

5.6 The Gram-Schmidt orthogonalization process. Exercises 1-4

- Thurs, Nov 25:

**Thanksgiving holiday; no class**

- Tues, Nov 30:

6.1 Eigenvalues and eigenvectors. Exercises 1-5

6.2 Systems of linear differential equations. Exercise 1

- Thurs, Dec 2:

6.3 Diagonalization. Exercises 1-4

6.4 Hermitian matrices. Exercises 1, 4

- Tues, Dec 7:

6.5 Quadratic forms. Exercises 1, 3

6.6 Positive definite matrices. Exercises 1, 3, 4

- Thurs, Dec 9:

exam review.

- Thurs, Dec 16:
**FINAL EXAM (chapters 5 and 6, some review questions)**