Introduction

Linear algebra has spectacular applications in disciplines as apparently diverse as computing, engineering and biology; moreover, it's at the core of much of pure mathematics. This course provides an introduction to linear algebra. As befits a 300-level course, it will involve a mixture of computation and proof, and of theory and application.

Logistics

Professor Jeff Achter
j.achter@colostate.edu
Weber 216, 491-6716
Lecture: MWF 9-9:50AM, Engrg E204
Office hours: TBA
Textbook: There is a recommended textbook, and a free, on-line text:
- Recommended: Introduction to Linear Algebra with Applications, Jim DeFranza and Daniel Gagliardi, McGraw-Hill 2009.
- Freely available: A First Course in Linear Algebra, by Robert Beezer.
More information about textbooks.

Requirements and other expectations

Homework and classwork -- 35% Homework will be assigned weekly, and is due at the beginning of class on Fridays. No late homework will ever be accepted. Your work must be neat, and the pages stapled, in order to be graded.
Midterms -- 40% There will be in-class exams on Friday, March 5 and ~~Friday, April 16~~ Monday, April 19.
Final -- 25% The final exam for this course will be held on Monday, May 10, 9:10-11:10AM.
No makeup exams will be given; you must take each exam as scheduled. You must pass the final in order to pass the course.

Help

This is challenging material, and you may need a little help every now and then.

Questions directed to j.achter@colostate.edu will be answered swiftly.
Professor Dick Painter will also hold common office hours for 369. (Time and location to be announced.)
Keep an eye on the news section of the page for more resources.

Topics

We will cover much of the material in the recommended textbook. Specifically, we will address systems of linear equations; matrix algebra; vector spaces and bases; linear transformations; eigenvalues and eigenvectors; and inner products.

As the course unfolds, the following table will indicate the relevant sections of the two textbooks.

Week Topic Beezer DeFranza and Gagliardi

1
1/18 Systems of linear equations
examples and applications; row reduction; echelon forms;
associated(augmented) matrices WILA What is Linear Algebra?
SSLE Solving Systems of Linear Equations
RREF Reduced Row-Echelon Form 1.1, 1.2

2
1/25 Solutions (cont.)
Matrix equations
Rⁿ; arithmetic of vectors; Ax=b
VO Vector Operations
MO Matrix Operations
MM Matrix Multiplication
1.3, 1.5, 2.1

3
2/1 Matrix equations
Inverses
Linear combinations HSE Homogeneous Systems
MISLE Matrix Inverses and Systems of Linear Equations
LC Linear Combinations
1.4 , 1.7 (p.68-72), 2.1, 2.2.

4
2/8 Spanning sets
Linear independence SS Spanning Sets
LI Linear Independence
LDS Linear Dependence and Spans
2.3, 3.2

5
2/15 Determinants DM Determinant of a Matrix
PDM Properties of Determinants of Matrices
1.6

6
2/22 Cramer's rule
Vector spaces fields; spaces; subspaces VS Vector Spaces 3.1, 3.2

7
3/1 Review

8
3/8 Independence; spanning set LISS Linear Independence and Spanning Sets
3.3

9
3/22 Bases; linear transformations B Bases
D Dimension
PD Properties of Dimension
LT Linear Transformations
3.3, 4.1

10
3/29 Nullspace, image
rank-nullity theorem Injective transformations
Surjective transformations
4.2

11
4/5 Bases and matrices VR Vector Representations
MR Matrix Representations
CB Change of Basis 4.4

12
4/12 Eigenvalues and eigenvectors;
review EE Eigenvalues and Eigenvectors
5.1

13
4/19 Midterm 2; characteristic polynomial

14
4/26 algebraic and geometric multiplicity;
diagonalizability and similarity;
inner products and norms Section O Orthogonality 5.2, 6.1, 6.2

15
5/3 Gram-Schmidt; triangle inequality;
orthonormal sets;
projection 6.3, 6.4

This page is available at http://www.math.colostate.edu/~achter/369

Week	Topic	Beezer	DeFranza and Gagliardi
1 1/18	Systems of linear equations examples and applications; row reduction; echelon forms; associated(augmented) matrices	WILA What is Linear Algebra? SSLE Solving Systems of Linear Equations RREF Reduced Row-Echelon Form	1.1, 1.2
2 1/25	Solutions (cont.) Matrix equations Rⁿ; arithmetic of vectors; Ax=b	VO Vector Operations MO Matrix Operations MM Matrix Multiplication	1.3, 1.5, 2.1
3 2/1	Matrix equations Inverses Linear combinations	HSE Homogeneous Systems MISLE Matrix Inverses and Systems of Linear Equations LC Linear Combinations	1.4 , 1.7 (p.68-72), 2.1, 2.2.
4 2/8	Spanning sets Linear independence	SS Spanning Sets LI Linear Independence LDS Linear Dependence and Spans	2.3, 3.2
5 2/15	Determinants	DM Determinant of a Matrix PDM Properties of Determinants of Matrices	1.6
6 2/22	Cramer's rule Vector spaces fields; spaces; subspaces	VS Vector Spaces	3.1, 3.2
7 3/1	Review
8 3/8	Independence; spanning set	LISS Linear Independence and Spanning Sets	3.3
9 3/22	Bases; linear transformations	B Bases D Dimension PD Properties of Dimension LT Linear Transformations	3.3, 4.1
10 3/29	Nullspace, image rank-nullity theorem	Injective transformations Surjective transformations	4.2
11 4/5	Bases and matrices	VR Vector Representations MR Matrix Representations CB Change of Basis	4.4
12 4/12	Eigenvalues and eigenvectors; review	EE Eigenvalues and Eigenvectors	5.1
13 4/19	Midterm 2; characteristic polynomial
14 4/26	algebraic and geometric multiplicity; diagonalizability and similarity; inner products and norms	Section O Orthogonality	5.2, 6.1, 6.2
15 5/3	Gram-Schmidt; triangle inequality; orthonormal sets; projection		6.3, 6.4