### 2017　Linear Algebra I / Recitation B（8～１3）

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Academic unit or major
Basic science and technology courses
Instructor(s)
Endo Hisaaki  Kawai Shingo
Class Format
Lecture / Exercise
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(W241)  Wed1-2(W241)  Fri1-2(W241)
Group
B（8～１3）
Course number
LAS.M102
Credits
2
Academic year
2017
Offered quarter
1Q
Syllabus updated
2017/3/17
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

Building on elementary facts about planar and spatial vectors learned at the high-school level, this course (with recitation) focuses on higher dimensional vectors and matrices, basics and applications of determinants, and systems of linear equations.

The aim of this course is to cover the basics of linear algebra, which will be fundamental for
science and engineering.

### Student learning outcomes

Students are expected to understand the basics of linear algebra (such as fundamental facts about matrices and determinants) which are necessary for studying science and engineering.

### Keywords

Vector, matrix, determinant, system of linear equations

### Competencies that will be developed

 Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

Theoretical materials are explained in lectures. A recitation class, with concrete examples and practice problems, is conducted every week.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Vectors, matrices, components Understand basics of vectors and matrices.
Class 2 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 3 Matrix operations Understand various operations on matrices.
Class 4 Regular matrix and inverse matrix Understand the notions of regular matrix and inverse matrix.
Class 5 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 6 Systems of linear equations and the elimination method Understand how to solve a system of linear equations.
Class 7 Elementary transformations and elementary matrices Understand elementary operations on matrices.
Class 8 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 9 General method for solving a system of linear equations Understand a more general method for solving a system of linear equations.
Class 10 Method of computing inverse matrices Understand how to compute inverse matrices.
Class 11 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 12 Rank of a matrix Understand the notion of rank for matrices.
Class 13 Definition of determinant up to order 3, geometric meaning of the determinant. Understand the definition of determinant and its meaning.
Class 14 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 15 Definition of determinant (arbitrary order), multi-linearity, alternating property Understand higher-order determinants.
Class 16 Method of computing determinants, special determinants Learn how to compute determinants.
Class 17 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 18 Expansion of determinants Understand determinant expansions.
Class 19 Determinant of transpose, multiplicativity Understand the determinant of a transposed matrix and of a product of matrices.
Class 20 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 21 Cramer's formula, formula for the inverse matrix Understand various useful formulas.
Class 22 Advanced topics Understand advanced topics on Linear Algebra.
Class 23 Recitation class is conducted parallel to the lectures. Help better understand the lectures.

### Textbook(s)

Linear Algebra, Murakami-Sato-Nozawa-Inaba, Baifukan

### Reference books, course materials, etc.

None in particular

### Assessment criteria and methods

Based on overall evaluation on the results of quizzes, reports, mid-term and final examinations. Details will be announced in class.

### Related courses

• LAS.M106 ： Linear Algebra II
• LAS.M108 ： Linear Algebra Recitation II

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

None in particular.

### Other

None in particular