Homework for Introduction to Linear Algebra

Math 40, Harvey Mudd College

Unless stated otherwise, all homework is due by 5pm in your instructors office box. Also, the Focus Problems listed below are problems that you should sincerely attempt to solve. They are good problems with which to grapple because they will help you better understand important and useful ideas and techniques. You will not submit your Focus Problem solutions, but be aware that the ideas addressed in the Focus Problems may appear on quizzes and exams.
1. Due Fri. 1/20: Vectors and Vector Spaces

2. Due Tue. 1/26: Systems of Linear Equations
Reading — Section 1.2 and 2.1.
Focus Problems — (2.1) 8, 10, 12, 22, 38, 40.
Problems — (1.2) 40, 42, 48, 50, 68, 70.

3. Due Fri. 1/29: Methods for Solving Linear Systems
Focus Problems — (2.2) 16, 19, 21, 23, 24, 40.
Problems — (2.2) 12, 14, 26, 28, 30, 42.

4. Due Tue. 2/2: Spanning Sets, Linear Independence, and Matrix Operations
Reading — Sections 2.3 and 3.1.
Focus Problems — (2.3) 4, 10, 22, 26, 44, 46.
Problems — (2.3) 8, 12, 24, 42. (3.1) 26, 38.

5. Due Fri. 2/5: Matrix Algebra and the Inverse of a Matrix
Reading — Sections 3.2 and 3.3.
Focus Problems — (3.1) 18, 24. (3.2) 26, 33. (3.3) 52, 54.
Problems — (3.2) 33, 36. (3.3) 19, 42, 46, 53

6. Due Tue. 2/9: Subspaces, Basis, Dimension, and Rank
Focus Problems — (3.5) 60, 61, 62, 63, 64, 65.
Problems — (3.5) 12, 18, 20, 46, 48, 58.

Due Mon. 2/15: Take Home Midterm
On Wednesday, February 10 a Take-Home Midterm will be distributed. It is due Monday, February 15, in class.

7. Due Tue. 2/16: Linear Transformations and Determinants
Reading — Sections 3.6 and 4.2.
Focus Problems — (3.6) 4, 8. (4.2) 1, 6, 12, 16.
Problems — (3.6) 6, 10, 20, 54.
Problems — (4.2) 8, 33.

8. Due Fri. 2/19: Determinants, Eigenvectors and Eigenvalues
Reading — Section 4.2 and 4.1.
Focus Problems — (4.2) 2, 4, 10, 40, 46, 56.
Problems — (4.1) 26, 35, 36.
Problems — (4.2) 14, 38, 54.

9. Due Tue. 2/23: Eigenvalues and Eigenvectors
Focus Problems — (4.3) 2, 4, 20, 26, 28, 40.
Problems — (4.3) 6, 8, 22, 24, 32, 34.

10. Due Fri. 2/26: Similarity and Diagonalization
Focus Problems — (4.4) 2, 4, 6, 24, 26, 28.
Problems — (4.4) 10, 12, 22, 44, 46, 48.

11. Due Tue. 3/1: Applications of Linear Algebra
Together with two other classmates, prepare a five minute presentation about an application of linear algebra that you find particularly interesting. Your presentation should be crafted so that your classmates can follow it using the knowledge they have gained as students in Math 40.

Your presentation should use 3-5 PDF slides that can be projected using a computer, and each member of your group should speak for roughly the same amount of time.

By 8:00 PM on Monday 2/29, for redundancy please submit your slides in two ways:
(1) email your instructor (one email per group);