Spring 2007 : M369 Linear Algebra (section 3)

  1. General information
  2. Prerequisites
  3. Textbook
  4. Homework and quizzes
  5. Exams
  6. Grading scheme
  7. Course syllabus

General information

Prerequisites

Prerequisites for this course are MCC161 (or M161) and M229. If you have taken equivalent courses elsewhere please see the instructor before registering.

Textbook

The textbook for this course is :

leon.jpeg

Steven J. Leon "Linear algebra with applications" 7th edition, Prentice Hall 2006.

It is available from the campus bookstore.

Homework and quizzes

There will be weekly homework, set from the textbook. The homework will be announced on Friday on this webpage (next to the syllabus), and must be handed in the following Wednesday at the beginning of the lecture.

There will usually be a short quiz at the beginning of Friday's lecture. This will test the concepts we have covered that week.

Exams

There will be two midterms and one final exam. These will all be held in the same room as the lectures (ENGRG E205).

If you are unable to attend any of these exams because of a legitimate reason (for example, it clashes with an exam for another course), then you must let the instructor know at least one week in advance.

Grading scheme

Your final grade will be determined from a score out of 600. The homework and quizzes will count for 200 points, the midterms will count for 100 points each, and the final exam will count for 200 points.

Course syllabus

The syllabus below will be updated as the semester progresses.

Week

Material covered (with page numbers)

Homework

Jan 15-19

Chapter 1 : Matrices and systems of equations

  • Systems of linear equations (1-11)
  • Row echelon form (13-25)
  • Matrix algebra (30-57)
  • Elementary matrices (61-69)

Page 12, exercises 6bdf, 10.
Page 25, exercises 2cde, 5f, 6ad, 10.
Page 57, exercises 2bd, 7, 10, 20a, 22.
Page 69, exercises 3ab, 10cef.
Due Wednesday 24th January.

Jan 22-26

Chapter 2 : Determinants

  • The determinant of a matrix (90-96)
  • Properties of determinants (98-103)
Chapter 3 : Vector spaces
  • Definition and examples (115-121)
  • Subspaces (123-131)

Page 97, exercises 3efg, 5.
Page 103, exercises 1ab, 2a, 7bc, 14.
Page 122, exercises 8, 10.
Page 131, exercises 1bcd, 3cdfg, 4b, 5ad, 10.
Due Wednesday 31st January.

Jan 29-Feb 2

Chapter 3 : Vector spaces

  • Linear independence (134-144)
  • Basis and dimension (145-150)

Page 144, exercises 2, 4bc, 5, 6bc, 14.
Page 150, exercises 3, 5, 7, 8, 10.
Due Wednesday 7th February.

Feb 5-9

Chapter 3 : Vector spaces

  • Change of basis (151-161)
  • Row space and column space (162-167)

Page 161, exercises 1b, 2b, 3b, 5, 6, 8.
Page 167, exercises 1c, 4cd, 7, 8, 10, 18.
Due Wednesday 14th February.

Feb 12-16

Chapter 4 : Linear transformations

  • Definition and examples (175-182)
  • Matrix representation of linear transformations (184-191)

Page 182, exercises 4, 5bc, 9, 15, 17, 22.
Page 196, exercises 4, 6, 14, 18ab.
Due Monday 19th February.

Feb 19-23

Chapter 4 : Linear transformations

  • Similarity (199-204)
Chapter 5 : Orthogonality
  • The scalar product in R^n (210-223)

Page 204, exercises 1ac, 4, 5, 8.
Due Friday 23rd February.
Practise for 1st Midterm Exam: postscript, pdf.
Solutions to the practise exam: postscript, pdf.
More practise for 1st Midterm Exam: postscript, pdf.
And the solutions: postscript, pdf.

Feb 26-Mar 2
1st Midterm
Wednesday 28th

Chapters 3 and 4 : Revision
Chapter 5 : Orthogonality

  • Orthogonal subspaces (225-232)

Page 223, exercises 3bd, 4, 6, 10.
Page 233, exercises 1d, 4, 6, 9, 13.
Due Wednesday 7th March.

Mar 5-9

Chapter 5 : Orthogonality

  • Least square problems (234-243)
  • Inner product spaces (245-252)

Page 243, exercises 1b, 3b, 4b, 5, 6, 10.
Page 252, exercises 2, 7, 8, 9.
Due Wednesday 21st March.

Mar 12-16

Spring Break

Mar 19-23

Chapter 5 : Orthogonality

  • Orthonormal sets (255-270)

Page 270, exercises 2, 3, 5, 7, 13b, 21, 28, 30.
Due Wednesday 28th March.

Mar 26-30

Chapter 5 : Orthogonality

  • The Gram-Schmidt orthogonalization process (274-281)
  • Orthogonal polynomials (283-289)

Page 281, exercises 3, 4, 5, 8, 11, 12.
Page 290, exercises 4, 5.
Due Wednesday 4th April.

Apr 2-6

Chapter 6 : Eigenvalues

  • Eigenvalues and eigenvectors (299-310)
  • Systems of linear differential equations (313-323)

Page 310, exercises 1cegj, 5, 9, 15, 19.
Page 323, exercises 2bc, 4.
Due Monday 9th April.

Apr 9-13

Chapter 6 : Eigenvalues

  • Diagonalization (325-340)
  • Hermitian matrices (344-352)

Page 340, exercises 1bd, 2bd, 3bd, 7, 9, 16.
Due Friday 13th April.
Practise for 2nd Midterm Exam: postscript, pdf.
Solutions to the practise exam: postscript, pdf.
More practise for 2nd Midterm Exam: postscript, pdf.
And the solutions: postscript, pdf.

Apr 16-20
2nd Midterm
Wednesday 18th

Chapter 5 and 6 : Revision
Chapter 6 : Eigenvalues

  • Hermitian matrices (344-352) cont.

Solutions to 2nd Midterm Exam: postscript, pdf.
Page 233, exercise 2.
Page 282, exercise 7.
Page 352, exercises 3, 5bcf, 11, 14, 22, 23.
Due Wednesday 25th April.

Apr 23-27

Chapter 6 : Eigenvalues

  • Singular value decomposition (355-369)

Page 369, exercises 2cd, 3, 4, 5, 7, 8.
Due Wednesday 2nd May.

Apr 30-May 4

Chapters 3, 4, 5, and 6 : Revision

Practise for the Final Exam: postscript, pdf.
Solutions to the practise exam: postscript, pdf.
More practise for the Final Exam: postscript, pdf.
And the solutions: postscript, pdf.
Note: You can ignore the problems about positive
definite matrices and Cholesky decompositions.

May 7-11
Final Exam
Wednesday 9th

Office hours Monday and Tuesday 1-4pm in Weber 114.
Reminder : The Final Exam will be in the usual room
ENGRG E205, from 7am to 9am.

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This page last modified by Justin Sawon
Friday, 04-May-2007 14:39:14 MDT
Email corrections and comments to sawon@math.colostate.edu