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Math 419-003 Linear Spaces and Matrix Theory


MW 8:30 - 10:00am   East Hall 3866
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Office Hours Syllabus Evaluation Handouts Homework Exams Reading
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Meetings!!!!


Meet your classmates here


  • Office hours will be held

  • In case you lost yours, or don't have it at hand:
    Syllabus

  • Please, let me know how you feel and what you think about the class as often as possible:

    You can email me and tell me, or just talk to me. I take critisicm very well.

    If you don't believe that, then you can send an anonymous evaluation .

  • Notation and definitions
  • Use of lin. alg. by Prof. Knill
  • To check your Gauss-Jordan elimination (for small square matrices) you can go here
  • If you're too lazy to write, check this out
  • Linear transformations , courtesy of Prof. A. Uribe

  • Your homeworks will be listed here. First list is the list of problems that will be collected. The second one is the list of problems that are recommended to be solved, but will not be graded.
    1. due on Wednesday, January 18.
      • Section 1.1: 28, 30.
      • Section 1.2: 12, 26, 34
      Suggested problems
      • Section 1.1: 32, 37, 40
      • Section 1.2: 18, 20, 21, 25, 40, 41

    2. due on Wednesday, January 25
      • Section 1.3: 8, 20, 24, 48.
      • Section 2.1: 24, 34, 42.
      • Section 2.2: 24, 28, 34
      Suggested problems
      • Section 1.3: 5, 16, 18, 29, 30, 47, 50.
      • Section 2.1: 5, 6, 13, 25--30.
      • Section 2.2: 9, 19, 20, 26, 38.

      Solutions to first and second homework.

    3. due on Wednesday, February 1
      • Section 2.3: 20, 36.
      • Section 2.4: 15, 18, 19, 20, 30, 35.
      • Section 3.1: 10, 14, 18, 24, 35, 38.

      Solutions to third homework.

    4. due on Wednesday, February 8
      • Section 3.2: 6, 24, 34, 36, 37, 50
      • Section 3.3: 22, 26, 31, 33, 38, 47.
      Suggested problems:
      • Section 3.2: 14--18, 30--32, 42
      • Section 3.3: 28, 32, 60, 61
      • Look into the True/False questions at the end of each chapter.
      Solutions to fourth homewrok.
      True/false

      Extra credit problem is due by Friday, 2/24, 4pm (my office). Prove the rank-nullity theorem:
      If V is a finite dimensional linear space and T a linear transformation from V to W, then dim(Im(T)) + dim(Ker(T))=dim(V).

    5. due on Wedensday, March 8.
      • Section 3.4: 27, 34, 39, 46, 48, 59.
      • Section 4.1: 5, 10, 12, 20, 31, 35, 37
      • Section 4.2: 7, 12, 24, 30, 36, 40, 56, 64
      Solutions to fifth homewrok.

    6. due on Wednesday, March 15
      • Section 4.3: 3,11,13,17,22,31,42,57.
      • Section 5.5: 4, 9, 14, 15
      • Section 5.1: 16,17, 23, 28
      Solutions to sixth homework.

    7. due on Wednesday, March 29
      • Section 5.2: 7, 18, 32, 39
      • Section 5.3. 25, 26, 28, 30, 36,
      • Section 5.4: 9, 22, 37.
      Solutions to seventh homework.

    8. due on Wednesday, April 5
      • Section 6.1: 19, 33, 41, 45, 46.
      • Section 6.2: 8, 29, 37, 46,
      • Section 6.3: 7, 9, 14, 24, 33, 36
      Solutions to eighth homework.

    9. due on Wednesday, April 12
      • Section 7.2: 10, 29, 32, 40, 43
      • Section 7.3: 10, 13, 17, 19, 21, 33, 35.
      • Section 7.4: 18, 20, 28, 33, 47, 51 -- do not turn in 47 and 51.
      Solutions to ninth homework.


  • The exams will be held in class.

  • Here is what I hope to be an accurate, but is most likely an approximate, schedule. The reason I give it is so that you can do your advance section reading without having an excuse "But you didn't tell us". My life, but more importantly your life, will be so much easier if you read each section the day before we get to it.


    Sec. Section title Date
    1.1 & 1.2 Introduction to linear systems & Matrices, vectors, Gauss-Jordan elimination 1/9
    1.2 & 1.3 Solutions of lin. systems Intro to lin. transformations 1/11
    finish 1.3 & 2.1/2.2 hw1 due Intro to lin. transformations and Lin. transformations in geometry 1/18
    2.2 & 2.3 Lin. transformations in geometry cont'd and Inverse of lin. transformation 1/23
    2.4 hw2 due Matrix products 1/25
    3.1 Image and kernel of lin. transformation 1/30
    3.2 hw3 due Subspaces, bases 2/1
    3.3 Dimension of subspace 2/6
    hw4 due Review 2/8
    Coordinates 2/13
    Midterm 2/15
    4.1&4.2 hw5 due Intro to linear spaces and lin. tranf. and isomorphisms 2/20
    4.3 hw5 due Matrix of lin. tranf. 2/22
    5.5 Inner product spaces 3/6
    5.1 hw6 due Orthogonal projections and orthonormal bases 3/8
    5.2 Review 3/13
    hw6 due Gram-Schmidt 3/15
    5.3&5.4 Orthogonal transf and matrices, least square fit 3/20
    Midterm 2 3/22
    6.1&6.2 hw7 due least square fit 3/27
    6.3&7.1 Determinants and their properties 3/29
    7.2&7.3 hw10 due Cramer rule and dynamical systems 4/3
    7.2&7.3 Eigenvalues and eigenvectors 4/5
    hw11 due Eigenvalues and eigenvectors 4/10
    7.5 Diagonalization 4/12
    Final Exam 4/17