Math 247
Linear Algebra I

Instructor

Ernest Boyd, Wissink 273, 389-1452
Office Hours:

Textbook

Linear Algebra and its Applications by David Lay

Course Content

We will look at problems introducing the kinds of mathematics used in studying linear systems. Topics include matrices, determinants, systems of linear equations, vector spaces, linear transformations, eigenvalues and eigenvectors. We will use the computer algebra system Mathematica. No previous experience with Mathematica is assumed. Prerequisite for Math 247 is one variable calculus; however, calculus is not used in this course.

Schedule

9:00 - 9:50 am, MTRF, Wissink Academic Computer Center Room 116 on MTR, Trafton C-311 on F

Tests

Thursday, Feb. 9

Thursday, Mar. 9

Tuesday, Apr. 18

Final Exam

Friday, May 12, 8 - 10 am

Grading Policy

Each test will be graded on its own scale normalized to 100%. At the end of the course the five grades will be averaged and compared to the average of the scales. Grading will reflect the mathematical correctness of the answer and the quality of the presentation in terms of completeness and organization. Active participation in the class discussions will also be factored into the evaluations. Make-up tests will be given only in special cases, when an excused absence has been prearranged. Incompletes will follow the university's policy as expressed in the student bulletins and the faculty handbook. No incomplete will be given to repeat the entire course.

MSU provides students with disabilities reasonable accommodation to participate in educational programs, activities or services. Students with disabilities requiring accommodation to participate in class activities or meet course requirements should first register with the Office of Disability Services, located in 0132 Memorial Library, telephone 389-2825, TDD 711 and then contact me as soon as possible.


Homework Assignments

  1. Page 11 #21-24, 33, 34.
    Page 25 #12, 13, 14, 23, 25, 27, 29.
    Hand in page 25 #34 on Friday, Jan. 27.
  2. Page 36 #9, 11, 18, 25, 28. Hand in #18 and 28 on Tuesday, Jan. 31.
  3. Page 47 #7, 9, 31, 32, 35, 36, 38. Hand in #38 on Friday, Feb. 3.
  4. Page 55 #7, 11, 23-28, 38, 39. Hand in #38 on Friday, Feb. 3.
  5. Page 63 #4.
  6. Page 116 #9-12, 22, 27, 37.
  7. Page 166 #3, 4, 5. Supplementary problems:
    1. If matrix A represents a rotation of the plane and matrix B represents a translation of the plane, does AB = BA? Illustrate it with Mathematica.
    2. If matrix A represents a rotation of the plane and matrix B represents a reflection of the plane over a line through the origin, does AB = BA? Illustrate it with Mathematica.
    3. If matrices A and B represent reflections of the plane over lines that intersect at the origin, what does AB represent? Illustrate it with Mathematica.
  8. Page 126 #13-24.
  9. Page 71 #12, 21, 22, 27, 28, 33-38. Hand in #34, 36 on Friday, Feb. 17.
  10. Page 132 #9, 16-24, 27, 28, 41, 42, 45. Hand in #22, 24 on Tuesday, Feb. 21.
  11. Page 173 #14, 25, 31-35. Hand in #14, 32, 34 on Friday, Feb. 24.
  12. Page 180 #14, 16, 30. Hand in these three problems on Monday, Feb. 27.
  13. Page 190 #21, 23, 24, 25, 27, 29, 37, 38.
  14. Page 199 #11, 15-20, 25, 31-36, 39, 40. Hand in #24, 32, 34, 36, 40 on Friday, Mar. 3.
  15. Page 308 #7, 15, 25. Hand in #25 on Tuesday, Mar. 7.
  16. Page 317 #13, 18, 19. Hand in #18 on Tuesday, Mar. 7.
  17. Page 341 #3, 15, 23, 24.
  18. Page 352 #9-14
  19. Page 296 #4, 14.
  20. Review
  21. Page 326 #23, 24, 34.
  22. Page 382 #5, 11, 24, 29, 30, 31. Hand in #24 on Friday, Mar. 24.
  23. Page 392 #9, 13, 29, 31, 32. Hand in #29 on Monday, Mar. 27.
  24. Page 400 #5, 9, 19.
  25. Page 407 #7, 12, 24. Hand in #24 on Friday, Mar. 31.
  26. Page 149 #6, 14.
  27. Prove det Q = ±1 for any orthogonal matrix Q. Hand in this problem on Monday, Apr. 3.
  28. Click Here Hand in these problems on Thursday, Apr. 6.
  29. Compute the Singular Value Decomposition for the matrix given in our Mathematica example without using Mathematica's SingularValues command.
  30. Page 426 #11, 13.
  31. Page 416 #12, 19-22. Hand in #12 on Friday, Apr. 14.
  32. Review
  33. Quiz on Thursday, Apr. 27.
  34. Page 223 #5, 6, 21. Hand in #8, 22 on Monday, May 1.
  35. Page 245 #33, 34, 37, 38. Hand in #34 on Monday, May 1.
  36. Page 253 #13, 33, 34. Hand in #34 on Tuesday, May 2.
  37. Page 261 #21 - 24. Hand in #24 on Tuesday, May 2.
  38. Page 276 #13, 14. Hand in #14 on Tuesday, May 2.

Mathematica Supplements

  1. Row Reduction
  2. Using LinearSolve
  3. Matrix Operations
  4. Translation of the Plane
  5. Rotation of the Plane
  6. Reflection of the Plane
  7. Glide Reflection of the Plane
  8. Spiral of the Plane
  9. Stretching of the Plane
  10. Hilbert Matrix and the Condition Number
  11. Leontief Input-Output Economic Model
  12. Determinant of a Square Matrix
  13. Eigenvalues and Eigenvectors of a Square Matrix
  14. Dynamical System
  15. Orthogonalization with Gram-Schmidt procedure
  16. Least Squares Method
  17. Matrix Decompositions
  18. Homework on LU and QR Decompositions
  19. Bases for the Vector Space of Polynomials
  20. Orthogonal Polynomials
  21. Simplex Algorithm
  22. Markov Chain

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