Fall 2006 : M369 Linear Algebra (section 1)

  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, mainly 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 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

Aug 21-25

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)
Chapter 2 : Determinants
  • The determinant of a matrix (90-96)
  • Properties of determinants (98-103)

As set by Prof Painter.
First set due Friday 25th August.
Second set due Monday 28th August.

Aug 28-Sep 1

Chapter 3 : Vector spaces

  • Definition and examples (115-121)
  • Subspaces (123-131)
  • Linear independence (134-144)


Third set due Friday 1st September.
Fourth set: page 144, exercises 1ace, 2bd, 5, 16.
Due Wednesday 6th September.

Sep 4-8
No class Monday
Happy Labor Day!

Chapter 3 : Vector spaces

  • Basis and dimension (145-150)
  • Change of basis (151-161)


Page 144, exercises 6ac, 7bd, 8.
Page 150, exercises 4, 5, 6, 10, 14.
Page 161, exercises 1b, 2b, 3b, 5, 6.
Due Wednesday 13th September.

Sep 11-15

Chapter 3 : Vector spaces

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

Page 161, exercises 8, 9.
Page 167, exercises 2ac, 3, 4abc, 5abc, 6, 7, 10, 14, 18, 19.
Due Wednesday 20th September.

Sep 18-22

Chapter 4 : Linear transformations

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

Page 182, exercises 1ae, 3, 4, 5ac, 6ac, 9a, 17ab, 18, 23.
Page 196, exercises 2ac, 3b, 6, 14, 18ac.
Due Wednesday 27th September.

Sep 25-29

Chapter 4 : Linear transformations

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

Page 204, exercises 1ad, 2, 3, 9.
Due Friday 29th September.
Practise for 1st Midterm Exam: postscript, pdf.
Solutions to the practise exam: postscript, pdf.
Review sheet and practise problems from Prof Oprea's class.

Oct 2-6
1st Midterm
Wednesday 4th

Chapters 3 and 4 : Revision
Chapter 5 : Orthogonality

  • Orthogonal subspaces (225-232)

Solutions to the 1st Midterm Exam: postscript, pdf.
Page 223, exercises 1a, 3c, 4, 8c, 9.
Page 233, exercises 1c, 2, 4.
Due Wednesday 11th October.

Oct 9-13

Chapter 5 : Orthogonality

  • Least square problems (234-243)

Page 233, exercises 5, 6, 9, 13.
Page 243, exercises 1ac, 2ac, 3b, 4b, 5, 6, 10.
Due Wednesday 18th October.

Oct 16-20

Chapter 5 : Orthogonality

  • Inner product spaces (245-252)
  • Orthonormal sets (255-270)

Page 252, exercises 1, 2, 3, 7, 8, 16.
Page 270, exercises 1bd, 2, 4, 5, 7, 9.
Due Wednesday 25th October.

Oct 23-27

Chapter 5 : Orthogonality

  • Orthonormal sets (255-270) cont.
  • The Gram-Schmidt orthogonalization process (274-281)

Page 272, exercises 14, 21ab(ii), 22ab(ii), 23, 27, 30.
Page 281, exercises 1b, 2b, 3, 5, 7, 11.
Due Wednesday 1st November.

Oct 30-Nov 3

Chapter 5 : Orthogonality

  • Orthogonal polynomials (283-289)
Chapter 6 : Eigenvalues
  • Eigenvalues and eigenvectors (299-310)
  • Systems of linear differential equations (313-323)

Page 290, exercises 4, 5.
Page 310, exercises 1adgk, 2, 4, 9, 11, 13, 27, 28a.
Page 323, exercises 1bc, 2b.
Due Wednesday 8th November.

Nov 6-Nov 10

Chapter 6 : Eigenvalues

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

Page 340, exercises 1acd, 2acd, 3acd, 4a.
Due Friday 10th November.
Practise for 2nd Midterm Exam: postscript, pdf.
Solutions to the practise exam: postscript, pdf.
Review sheet from Prof Oprea's class.

Nov 13-Nov 17
2nd Midterm
Wednesday 15th

Chapter 5 : Revision

Chapter 6 : Eigenvalues

  • Hermitian matrices (344-352) cont.

Solutions to the 2nd Midterm Exam: postscript, pdf.
Page 341, exercises 8ab, 9, 26ab, 27b, 28c.
Page 352, exercises 2, 3, 5bcf, 11, 14.
Due Wednesday 29th November.

Nov 20-Nov 24

Thanksgiving

Nov 27-Dec 1

Chapter 6 : Eigenvalues

  • Singular value decomposition (355-369)
  • Quadratic forms (370-383)

Page 369, exercises 2bc, 3(only for the matrices in 2bc), 4, 5, 8.
Page 383, exercises 2, 3ad, 4, 6bde, 8, 14.
Page 390, exercises 3, 4ac, 5ac, 9.
Due December 6th December.

Dec 4-Dec 8

Chapter 6 : Eigenvalues

  • Quadratic forms (370-383) cont.
  • Positive definite matrices (384-390)
Chapters 3, 4, 5, and 6 : Revision

Practise for the Final Exam: postscript, pdf.
(The actual final exam will be slightly shorter than this.)
Solutions to the practise exam: postscript, pdf.
Sample exam from Prof Oprea's class.

Dec 11-Dec 15
Final Exam
Tuesday 12th

Office hours Monday 12noon-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
Tuesday, 16-Jan-2007 12:48:50 MST
Email corrections and comments to sawon@math.colostate.edu