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Homework for Introduction to Linear Algebra

Math 40, Harvey Mudd College

Unless stated otherwise, all homework is due at the beginning of class. 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.

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1. Due Fri. 1/20: Vectors and Vector Spaces

Reading — Sections 1.1, 1.2, a note about Communicating Mathematics through Homework, and Prof. Su's Notes on Writing Mathematics Well.
Focus Problems — (1.2) 17, 18, 52, 56, 58, 60.
Problems — (1.2) 5, 9, 15, 17, 18, 30.

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2. Due Wed. 1/25: 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.

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3. Due Fri. 1/27: Methods for Solving Linear Systems

Reading — Section 2.2.
Focus Problems — (2.2) 16, 19, 21, 23, 24, 40.
Problems — (2.2) 12, 14, 26, 28, 30, 42.

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4. Due Wed. 2/1: 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.

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5. Due Fri. 2/3: 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) 32, 36. (3.3) 19, 42, 46, 53

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6. Due Mon. 2/6: Take Home Midterm

On Friday, February 3 a Take Home Midterm will be distributed. It is due Monday, February 6 in class.

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7. Due Fri. 2/10: Subspaces, Basis, Dimension, and Rank

Reading — Section 3.5.
Focus Problems — (3.5) 60, 61, 62, 63, 64, 65.
Problems — (3.5) 12, 18, 20, 46, 48, 58.

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8. Due Wed. 2/15: 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.

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9. Due Fri. 2/17: 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.

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10. Due Wed. 2/22: Eigenvalues and Eigenvectors

Reading — Section 4.3.
Focus Problems — (4.3) 2, 4, 20, 26, 28, 40.
Problems — (4.3) 6, 8, 22, 24, 32, 34.

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11. Due Fri. 2/24: Similarity and Diagonalization

Reading — Section 4.4.
Focus Problems — (4.4) 2, 4, 6, 24, 26, 28.
Problems — (4.4) 10, 12, 22, 42, 44, 46.

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12. Due Tue. 2/29: 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 25.

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 Tuesday 2/29, for redundancy please submit your slides in two ways:
(1) email your instructor (one email per group);
(2) upload your slides to the Dropbox section of your Sakai site (one upload per group).
Be prepared to speak on Wednesday or Friday.

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