Course title
Q14104001
Linear Algebra 1

 KAJIGAYA Toru
Course description
Linear algebra is a fundamental mathematics in the field of science and engineering. In this lecture, students will learn the definition of a matrix and its basic operations, and then learn the general theory of simultaneous linear equations and computation of inverse matrices as applications. Students will also learn about determinants and their properties, linear transformations on the plane and diagonalization of square matrices and its meaning.
Purpose of class
Students will master the basic operations of matrices. Furthermore, to solve simultaneous linear equations by Gaussian elimination and to understand the relationship between the type of solution and the rank of matrix. To be able to compute determinants and determine the properties of matrices using determinants. To understand linear transformations on the plane and diagonalization of square matrices.
Goals and objectives
  1. To be able to basic operations for matrix
  2. To be able to understand linear transformation on the plane and diagonalize 2x2 matrices.
  3. To be able to solve simultaneous linear equations by Gaussian elimination and to understand relation between type of solution and rank of the coefficient matrix.
  4. To be able to compute the determinant of 3x3 matrices.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term exam Final exam Total.
1. 20% 10% 30%
2. 10% 10% 20%
3. 10% 20% 30%
4. 0% 20% 20%
Total. 40% 60% -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Vector and its calculations Review of high-school mathematics 200minutes
2. Matrix and its calculations (1) Review of the last lecture 180minutes
3. Matrix and its calculations (2) Review of the last lecture 180minutes
4. Linear transformation on plane and diagonalization of square matrices Review of the last lecture 180minutes
5. Gaussian elimination Review of the last lecture 200minutes
6. Rank of matrix Review of the last lecture 180minutes
7. Simultaneous linear equations (1) Review of the above 180minutes
8. Mid-term exam and its feedback Review of the last lecture 240minutes
9. Simultaneous linear equations (2) Review of the last lecture 180minutes
10. Computing the inverse matrix Review of the last lecture 180minutes
11. Determinants and their properties Review of the last lecture 180minutes
12. Cofactor expansion Review of the last lecture 180minutes
13. Application of determinants Review of the last lecture 180minutes
14. Final exam and its feedback Review of the above 240minutes
Total. - - 2680minutes
Evaluation method and criteria
The mid-term exam will be evaluated as 40%, the final exam as 60%. Students will pass the class when they are judged to have understood at least 60% of the content covered in the class (total score: 60 points or more).
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
教科書：三宅敏恒著、入門線形代数、培風館
参考書：長谷川浩司著、線型代数、日本評論社
Prerequisites
Calculation of vectors
Office hours and How to contact professors for questions
  • Basically, I will respond before or after class or by e-mail. The email address will be provided in class.
  • Please make active use of the Study Support Room (Physics and Mathematics).
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Sat Mar 22 04:07:43 JST 2025