| Instructor: | Dr. Douglas Anderson |
| Ivers 234G | |
| 299-4453 (office), 299-4151 (math department) | |
| andersod@cord.edu |
Office Hours: TuTh 1:00-4:00, other times by discovery.
Text: Introductory Linear Algebra with Applications, 8th edition, by Bernard Kolman and David R. Hill, ISBN 0131437402.
Prerequisite: Math 122 (Calculus II) or equivalent.
Purpose: There are many ways to study linear algebra. For example, we could focus on computational matrix algebra and its applications to calculus, differential equations, the physical and social sciences, economics, and so on. Or we could concentrate on the broader topic of linear theory and general vector space structure. These and many other approaches could easily fill several semesters of study. Having only one semester at hand, we will strike a balance between mathematical reasoning on the one hand, and linear systems and vector spaces on the other; a few applications will be done as time permits. With nearly half of our emphasis being theoretical in nature, we consider this course to be the first real transition course to mathematical proof. The reliance on rational, rigorous proof is a hallmark and strength of mathematical inquiry, a reliance we will develop and expect in this course. By studying the mathematical vocabulary and the logical structure of the foundation of linear algebra, we learn the fundamental logic of deductive and inductive reasoning; encounter and construct proofs of elementary theorems using direct, indirect, existence, and inductive arguments; and understand the role of mathematical definitions and counter examples. Topics in linear algebra include systems of linear equations, matrices, determinants, vectors in n-space, abstract vector spaces, and linear transformations.
Homework: Homework will be assigned each day for your development toward mastering the material, and will be due
two class periods later. I will allow up to four (4) late submissions without penalty; after that late homework will not
be accepted. Your final homework write-up must be neat and organized. You will not only be graded on correct
answers but also on the neatness, organization, steps used to derive your answers, and the use
of correct English grammar and complete sentences. All students must abide by the college's
expectations regarding academic integrity.
Exams: Attendance is required for all exams. If you should miss an exam for an emergency you
will be allowed to make it up only if you have notified me before the exam and it
must be made up in a timely manner (to be discussed with me individually). I will give you at
least one week notice before the exams. The comprehensive final exam is scheduled for
8:30-10:30 a.m. Friday, April 30.
| Grading: | Points | Scale | |||
| Homework | 150 | A 90%--100% | |||
| Exams(3) | 300 | B 80%--89% | |||
| Final Exam | 200 | C 70%--79% | |||
| D 60%--69% | |||||
| F Below 60% |
| Date | Section | Exercises |
| Jan 3 | 1.1 Linear Systems | (8) 1-3,8,10,12,15,19,20,26(see ex 7, pg 7), T.4 |
| 5 | No Class | Read pages 10-18 |
| 7 | No Class | (19) 2-4,7,8,9,11, T.6 (see T.5), T.13, T.16 |
| 10 | 1.3 Dot Product | (34) 1-3,5-8,11,15,26-28,31, T.1, T.3, T.10 |
| 12 | 4.1 Vectors | (227) 2,5ab,6ab,8,9ab-12ab,19ab-22ab, T.4, T.8 |
| 14 | 4.2 n-vectors | (244) 10,20ac,24,25,28ac,32, T.5, T.6, T.8 |
| 17 | Proof Techniques | Handout |
| 19 | Proofs continued | Handout |
| 21 | 1.4 Matrix Properties | (49) 2,3,10,11,13a,16,18,19, T.6, T.8, T.16, T.23, T.27(see T.24), T.40 |
| 24 | 4.3 Linear Transformations | (255) 1,3,5,7,11,17,19,23 |
| 26 | Review | (258) Chapter Test 1,2,5,6; proofs |
| 28 | Exam 1 | |
| 31 | 1.6 Linear Systems | (85) 18,20ab,21ac,22ad,31,32,39 |
| Feb 2 | 1.6 Linear Systems | (86) 23-28,37,38, T.5, T.6, T.11ad |
| 4 | 1.7 Matrix Inverse | (105) 1-4,5b,6ab,11,16,19,20,25,26, T.1, T.10 |
| 7 | 6.1 Vector Spaces | (278) 2,4,11,12,17, T.1, T.3, T.4 |
| 9 | 6.1 Vector Spaces | continued |
| 11 | 6.2 Subspaces | (287) 5,6,8,10,16ab,18-20,25-27, T.7, T.8 |
| 14 | 6.3 Independence | (301) 1,2,4,10,11ab,12ac, T.5, T.6, T.7, T.10 |
| 16 | 3.1 Determinants | (193) 6abc,8,11-16,20,22,23, T.3, T.5, T.6, T.8, T.10, T.14, T.15 |
| 18 | 3.2 Determinant Applications | (208)5,15,17,19, T.10 |
| Mar 4 | Review | (118) 1-6,8; (213) 1-6; (374) 1,4,6abc |
| 7 | Exam 2 | |
| 9 | 6.4 Basis | (314) 7,8,11-14,17-19,30,32 |
| 11 | 6.4 Dimension | (314) 1,2,21,24, T.3, T.10, T.12, T.13, T.14 |
| 14 | 6.5 Homogeneous Systems | (327) 3-9,13,16,17,20, T.1(hand in), T.2 |
| 16 | 6.6 Rank | (337) 1,2,6,8,13,15,16,18-22, T.6 |
| 18 | 6.7 Change of Basis | (349) 1-5,7-10,21-24, T.2, T.3 |
| 21 | 6.8 Orthonormal Bases | (359) 1-6,11,15,16,17,18, T.5, T.6 |
| 23 | 6.9 Orthogonal Complements | (369) 1,4a,5,8a,10,12,14 |
| 25 | Good Friday | No Class |
| 28 | Easter Monday | No Class |
| 30 | 7.2 Least Squares | (388) 1,2,7,8,14 |
| Apr 1 | 8.1 Eigenpairs | (420) 1,2,6,9-12,20, T.1, T.5(hand in), T.8 |
| 4 | 8.2 Diagonalization | (431) 1,3,5,7,9,15,17,23,33, T.2, T.6, T.10 |
| 6 | Review | (374) 2-5,6c-j; (407) 4,5; (445) 1,3,4,7 |
| 8 | Exam 3 | |
| 11 | 8.3 Symmetric Matrices | (443) 1,2,4-7,14, T.4, T.6, T.7 |
| 13 | 9.5 Conic Sections | (491) 19,22,24 |
| 15 | 10.1 Linear Transformations | (507) 2,3,6,7,12,18, T.6, T.10 |
| 18 | 10.2 Kernel | (519) 1,3,5, T.4, T.7 |
| 20 | 10.2 Range | (519) 7,11,15,17,19, T.6, T.8 |
| 22 | Review | (520) T.1,5,9,10,11, (555) 1-100 |
| 25 | Review | (446) 1-4; (554) 1-4,6; Exams 1-3 |
| 29 | Final Exam | Friday, 8:00-10:30 |
Key Equivalences in Linear Algebra: Let A be an nxn matrix.
|
A is nonsingular A is invertible rref(A)=I, A and I are row equivalent A has n (nonzero) pivots A inverse exists Ax=0 has only the trivial solution Ax=b has unique solution x=A^(-1)b Determinant of A is nonzero Rows of A are linearly independent Row space of A is R^n Rank(A)=n Columns of A are linearly independent Column space of A is R^n Nullity of A is 0 All eigenvalues of A are nonzero |
A is singular |