MATH 240 Linear Algebra with Applications

Spring 2005 Prof. Raymond Johnson

• Office Hours

Grades will be based on four hour exams counting 100 points each, homework, quizzes and MATLAB projects worth 200 points, and a final examination that is worth 200 points.

The class meets according to the following schedule:

Monday, Wednesday, and Friday, 11:00-12:00

Armory 0131.

TOPICS

Systems of Linear Equations

Gaussian elimination

Matrix operations

Finding the inverse

Solution spaces

Determinants

Definition

Evaluation

Minors

Cramer's Rule

Vectors in 2- and 3- space

Geometric and algebraic definitions

Dot product

Projections

Vector Spaces

Euclidean space

Subspaces

Linear independence

Basis and dimension

Row space, rank

Length and angle

Gram-Schmidt

Least squares

Linear Transformations

Definition

Kernel and range

Representation as matrices

Eigenvalues and Eigenvectors

Definition

Diagonalization

Orthogonal diagonalization

Symmetric matrices

Applications

Differential equations

Quadratic forms

Numerical methods

Sections are from LInear Algebra with Applications, 3rd edition by Lay.

Suggested homework problems.

You should at least be able to work these problems; some of them may later be assigned to be turned in. The dates are dates by which time you should have completed the assignment, in order to keep pace with lecture.

Due Date Exercises (Text 3rd Edition)

• 1. 1/28 1.1: 1-15(odd), 19-25(odd), 26
• 2. 2/1 1.2: 3, 5, 6, 7-15(odd), 19, 23, 24, 25; 1.3: 1, 3 (Read to p. 32)
• 3. 2/3 1.2: 27, 30, 31; 1.3: 5-21(odd) (#5 ans may be incorrect); 1.4: 1-11(odd) (Read to p. 43)
• 4. 2/8 1.3: 25, [28], 31a, 32; 1.4: 13, 15, 18, 20, 21; 1.5: 1-9(odd), (Read to p. 51)
• 5. 2/10 1.4: 25, 27, 31, 35, [40]; 1.5: 11, 14, 15(odd), 18, 19, 33; 1.7: 1-9(odd) (Read to p. 66)
• 6. 2/14 (Mon) 1.5: 29, 30, 31, 32, 36; 1.7: 11-19(odd); 1.8: 1-11(odd), 17, 18, 19 (Read to p. 78)
• 7. 2/15 (Tue) 1.7: 24, 26, 31-37(odd), [42], [44]; 1.8: 25, 27, 31; 1.9: 1-13(odd) (Read to p. 86)
• 8. 2/17 (Thu) 1.9: 15-21(odd); 1.10: 9, 10, [12] (Read pages 97-99) .
• 2/18 (Fri) FIRST HOUR EXAM
• 9. 2/22 (Tue) 1.8: 25-31(odd), 32, 35, [38]; 2.1: 1-13(odd), 17-25(odd) Learn proof of Theorem 2(a). (Read to p. 107)
• 10. 2/24 (Thu) 2.1: 24, 29, 30, 32, [35], [36]; 2.2: 3, 6, 7, 11, 13, 16, 19, 21, 23 (Omit pages 114-116, but study Theorem 7 as discussed in class)
• 11. 2/28 (Mon) 2.2: 15, 17, 18, 24, [41]; 2.3: 1, 3, 5, 7, 9, 15-31(odd); 2.4: 1, 3 (Read to p. 128)
• 12. 3/1 (Tue) 2.1: 20, 22; 2.3: 16, 18, 20, [37]; 2.4: 5, 7, 9, 13, 17, [24]
• MATLAB 1: : 1.8: [38]; 2.1: [35], [36] 2.2: [41]; 2.3: [37]
• 13. 3/3 (Thu) 2.3: 22, 24, 26, [38]; 2.8: 1-11 (odd), [22]
• 14. 3/7 (Mon) 2.8: 13, 15, 17; 3.1: 1, 9, 11, 15-21 (odd), 25-35 (odd), [43], [45]
• 15. 3/8 (Tue) 2.9: 1, 3, 5, 9, 11, 13, 15, 17, 19 3.1: 37, 41; 3.2: 1-7(odd), 13-25(odd), 31, 33 (Omit linearity on p. 191)
• 16. 3/10 (Thu) 3.2: 35, 39; 3.3: 19-27(odd) (Read pages 199-204)
• 3/11 (Fri) SECOND HOUR EXAM
• 17. 3/15 (Tue) 4.1: 1, 2, 4, 5-19(odd), 25, 27, 31, 32, [33], [35]; 4.2: 1, 3, 7, 9, 11, 13, 15, 17, 19, 21, 23, 27, 29
• 18. 3/17 (Thu) 4.2: 31, 34, 35, [39]; 4.3: [18], 19, 23, 25, 27, 28, 31, [34]; 4.4: 1-7(odd), [34]
• SPRING BREAK
• 19. 3/29 (Tue) 4.3: 28, 31; 4.4: 9, 11, 13, 17, 25, 27, 29, 32; 4.5: 1-9(odd), 11-17
• MATLAB 2: : 2.3: [38]; 2.4: [24]; 2.8: [22]; 3.1: [43], [45]
• 20. 3/31 (Thu) 4.4: 27, 29, [32]; 4.5: 11-17(odd), 21-27(odd); 4.6: 1-9(odd), 13
• 21. 4/4 (Mon) 4.5: 29, [33], [34]; 4.6: 11, 15, 19, 21, 23, 27, 31, 32; 4.7: 1, 3, 5
• 22. 4/5 (Tue) 4.6: 20, 25; 4.7: 7, 9, 13, [17], [18]; 4.9: 1, 5, 7, 11
• 23. 4/7 (Thu) 4.9: 13, 14, [16]
• 4/8 (Fri) THIRD HOUR EXAM
• 24. 4/12 (Tue) 5.1: 1-9(odd), 13, 15, 17, 19, 23, 33, [37]
• 25. 4/14 (Thu) 5.2: 1-7(odd), 15, 17, 25; 5.3: 1, 3
• MATLAB 3: : 4.4: [33]; 4.5: [33], [34]; 4.7: [17], [18]
• 26. 4/18 (Mon) 5.2: 19, 27; 5.3: 5-17(odd), 18, 23-29(odd), [34]; 5.4: 1-7(odd)
• 27. 4/19 (Tue) 5.4: 25, 26, 27 (Read p. 325); 5.5: 1, 3, 5
• 28. 4/21 (Thu) 5.4: 11, 13, [32];
• 29. 4/25 (Mon) 5.6: 1, 3, 5, 7-15(odd), [16]; 6.1: 1-17(odd)
• 30. 4/26 (Tue) 5.6: 17ab; 6.1: 21, 25, 26, 28; 6.2: 1-15(odd)
• 31. 4/28 (Thu) 6.1: 31; 6.2: 17, 19, 21, 25
• 4/29 (Fri) FOURTH HOUR EXAM
• 32. 5/3 (Tue) 6.2: 26, 27 6.3: 1-15(odd), 19, [25] (Note for [25]: U is from Exercise 34 in Section 6.2.)
• 33. 5/5 (Thu) 6.3: 17; 6.4: 1-15(odd), [22], [23]
• 34. 5/9 (Mon) 6.5: 1, 3, 4, 7, 9, 13, 14, 15, 25;
• 35. 5/11 (Thu) 7.1: 1-27(odd) 7.2: 1-7(odd)
• 36. 5/15 (Mon) 7.1: 29; 7.2: 7-9, 11, 13, 21;
• 5/16 (Mon) FINAL EXAM

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