### Linear Algebra I University of Tsukuba

#### Course Overview

This course introduces the basic ideas of vector, matrix and their operations and how to solve linear equations using matrices and vectors. The primary goal of this course is to understand the systems of linear equations, classifications of matrices and their applications. Although most of the problems can be solved without Mathematica, you are encouraged to solve the homework using the software once you know how to solve the problems. The course is a prerequisite for “Linear Algebra II”

#### Learning Achievement

This course introduces the basic ideas of vector, matrix and their operations and how to solve linear equations using matrices and vectors. The primary goal of this course is to understand the systems of linear equations, classifications of matrices and their applications. Although most of the problems can be solved without Mathematica, you are encouraged to solve the homework using the software once you know how to solve the problems. The course is a prerequisite for “Linear Algebra II”

#### Competence

Related to 1. Mathematical logic and calculation skills.

#### Course prerequisites

Math B at high school in Japan.

#### Grading Philosophy

Quiz + homework 30%

Midterm Exam 35 %

Final Exam 35%

#### Course schedule

Introduce vectors and its operation

Introduce matrix and related matrix ？vector to linear equation

The idea of elimination and elimination using matrices

Rules of Matrix Operations and Inverse of Matrices

Review Inverse of Matrices and Exercises

Elimination (Factorization:) A=LU

Transpose and Permutations

Review and midterm examination

Answer to midterm exam and Spaces of Vectors

The Null spaces of A

The Complete Solution to Ax=b + review

Independence, and Dimension of the Four subspaces

Orthogonality of the Four Subspaces and Projections

Least squares approximations and Orthonormal Bases

Applications: Graphs and Networks + Review

#### Course type

Lectures and Class Exercises

#### Online Course Requirement

#### Instructor

Tong Xiao-Min

#### Other information

*You are encouraged to discuss with others about the contents of the course and homework, but you must work out the homework yourself. No late homework will be accepted.

* All exams are closed book and you cannot use notes, calculators during the exams.

#### Site for Inquiry

Link to the syllabus provided by the university