Syllabus Number
Course
Name
Semester, Year
Linear Albegra I
First, 2015
Course level
Instructor(s)
(Institution)
Course
Objectives
Course Goals
Course
Schedule
Homework
Grading
System
Textbooks /
Reading List
Additional
Information
Number of Credits
2 credits
Course Number
Simona Settepanella
This course covers basic knowledge on matrices, linear equations and determinants.
The ability:
- to master computations on matrices (sums, inverse matrices, rank, etc…);
- to solve systems of linear equations;
- to compute determinants.
A precise understanding of relations between the above notions.
Week 1
Matrices -- Definitions, examples.
Week 2
Matrices -- Addition, scalar multiplication, linear combinations, multiplication.
Week 3
Matrices -- Square Matrices, inverses and zero divisors.
Week 4
Matrices -- Transposes, partitioning of matrices and direct sums.
Week 5
System of linear equations -- Equivalent systems of equations, row operations on Matrices, row echelon
form.
Week 6
System of linear equations -- Homogeneous systems of equation, rank, arbitrary systems of equations.
Week 7
System of linear equations – A general solution for arbitrary systems of equations, inverses of non
singular matrices.
Week 8
Determinants – Introduction as a volume functions, permutations, sign of permutations.
Week 9
Determinants -- Definition, basic properties, practical evaluation and transposes of determinants.
Week 10
Determinants -- cofactors, cofactor matrix, expansions.
Week 11
Determinants -- Cramer formula, Vandelmonte matrix, determinants and ranks.
Week 12
Computations I.
Week 13
Computations II.
Week 14
Relation with Geometry (Rotation, reflection, binary forms).
Week 15
Relation with Geometry (volume of parallelepiped, exterior product).
Study at home at least two hours per week -- Check basic notions you learn in the course,
and try to solve exercises assigned by the teacher.
Students are graded accordingly to whether or not
1. he/she masters basic knowledge (definitions, theorems etc);
2. he/she can correctly answer questions;
3. he/she is able to apply the knowledge achieved during the course to given problems.
The textbook of the course is “Matrices and Linear Algebra” by H. Schneider and G.P.
Barker. Edited by Dover.
Students can buy the book: “The Manga Guide to Linear Algebra” by Shin Takahashi. It is
facultative, but recommended to students who are unfamiliar with mathematics.
Additional information can be found on the Instructor’s home page:
http://www.math.sci.hokudai.ac.jp/~s.settepanella/
Syllabus Number