### 2016　Linear Algebra I / Recitation

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Academic unit or major
Basic science and technology courses
Instructor(s)
Ma Shohei  Takasawa Mitsuhiko
Course component(s)
Lecture / Exercise
Day/Period(Room No.)
Mon1-2(W521)  Wed3-4(W521)  Fri3-4(W521)
Group
G(41〜47)
Course number
LAS.M102
Credits
2
Academic year
2016
Offered quarter
2Q
Syllabus updated
2017/1/11
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 Unit matrix, symmetric matrix, diagonal matrix, triangular matrix Understand the definition of various matrices.
Class 4 Matrix operations Understand various operations on matrices.
Class 5 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 6 Regular matrix and inverse matrix Understand the notions of regular matrix and inverse matrix.
Class 7 Systems of linear equations and the elimination method Understand how to solve a system of linear equations.
Class 8 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 9 Elementary transformations and elementary matrices Understand elementary operations on matrices.
Class 10 General method for solving a system of linear equations Understand a more general method for solving a system of linear equations.
Class 11 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 12 Method of computing the inverse of a matrix Understand how to compute inverse matrices.
Class 13 Rank of a matrix Understand the notion of rank for matrices.
Class 14 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 15 Definition of determinant up to order 3, geometric meaning of the determinant. Understand the definition of determinant and its meaning.
Class 16 Definition of determinant (arbitrary order), multi-linearity, alternating property Understand higher-order determinants.
Class 17 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 18 Method of computing determinants, special determinants Learn how to compute determinants.
Class 19 Expansion of determinants Understand determinant expansions.
Class 20 Recitation class is conducted parallel to the lectures. Help better understand the lectures.
Class 21 Determinant of transpose, multiplicativity Understand the determinant of a transposed matrix and of a product of matrices.
Class 22 Cramer's formula, formula for the inverse matrix Understand various useful formulas.
Class 23 Recitation class is conducted parallel to the lectures. Help better understand the lectures.

### Textbook(s)

MatsuzakaKazuo`Senkeidaisunyumon'

### Reference books, course materials, etc.

None in particular

### Assessment criteria and methods

Assessment is based on the results of quizzes, homework, mid-term and final examinations. Details will be announced in lecture.

### Related courses

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

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

None in particular. 